View
15
Download
1
Category
Preview:
Citation preview
Name____________________________
Precalculus Teacher_________________________
Practice
Packet
Unit 6 Sequences & Series
Unit 6 Learning Targets
Unit 6 Learning Targets
Number Chapter and Section Title Description
LT1 10.1 Sequences and Summation Notation
Find particular terms of a general or recursive sequence using the general formula.
LT2 10.1 Sequences and Summation Notation
Evaluate a factorial expression.
LT3 10.1 Sequences and Summation Notation
Given terms in a sequence, create the general or recursive formula.
LT4 10.1 Sequences and Summation Notation
Given summation notation, evaluate the sum.
LT5 10.1 Sequences and Summation Notation
Express a sum using summation notation.
LT6 10.1 Sequences and Summation Notation
Given a set of terms, write the sum using sigma notation.
LT7 10.2 Arithmetic Sequences Find particular terms of an arithmetic sequence using the general formula.
LT8 10.2 Arithmetic Sequences Determine the common difference for an arithmetic sequence.
LT9 10.2 Arithmetic Sequences Given terms in a sequence, create the arithmetic formula.
LT10 10.2 Arithmetic Sequences Evaluate the sum of a finite arithmetic series.
LT11 10.3 Geometric Sequences Find particular terms of a geometric sequence using the general formula.
LT12 10.3 Geometric Sequences Determine the common ratio for a geometric sequence.
LT13 10.3 Geometric Sequences Given terms in a sequence, create the geometric formula.
LT14 10.3 Geometric Sequences Evaluate the sum of a finite or infinite geometric series.
LT15 10.3 Geometric Sequences Identify if a sequence is arithmetic, geometric, or neither.
LT16 10.5 Binomial Theorem Evaluate a binomial coefficient.
Unit 6 Learning Targets
LT17 10.5 Binomial Theorem Expand a binomial raised to a power.
LT18 10.5 Binomial Theorem Find a particular term in a binomial expansion.
LT19 10.5 Binomial Theorem Find the coefficient only of the indicated term of the given binomial.
Learning Targets 1-6 Unit 6: Sequences and Summation Notation Practice 10.1
Unit 6 Practice Page 1
Write the first four terms of each sequence whose general term is given.
1. an = 3n + 2 2. an = 3π
_____ _____ _____ _____ _____ _____ _____ _____
3. an = (β3)π 4. an = (β1)π(π + 3)
_____ _____ _____ _____ _____ _____ _____ _____
5. an =2π
π+4 6. an =
(β1)π+1
2πβ1
_____ _____ _____ _____ _____ _____ _____ _____
Write the first four terms of each sequence defined using recursion formulas.
7. an = ππβ1 + 5 πππ π β₯ 2 ππ π1 = 7 8. an = 4ππβ1 πππ π β₯ 2 ππ π1 = 3
_____ _____ _____ _____ _____ _____ _____ _____
9. an = 2ππβ1 + 3 πππ π β₯ 2 ππ π1 = 4 10. an = 3ππβ1 β 1 πππ π β₯ 2 ππ π1 = 5
_____ _____ _____ _____ _____ _____ _____ _____
Learning Targets 1-6 Unit 6: Sequences and Summation Notation Practice 10.1
Unit 6 Practice Page 2
The general term of a sequence is given and involves a factorial. Write the first four terms of each.
11. an =π2
π! 12. an = 2(n + 1)!
_____ _____ _____ _____ _____ _____ _____ _____
Evaluate each factorial expression. Show your work.
13. 17!
15! __________ 14.
16!
2!14! __________
15. (n+2)!
n! __________ 16.
(2n+1)!
(2n)! __________
17. A deposit of $6000 is made in an account that earns 6% interest compounded quarterly. The balance in the
account after n quarters is given by the sequence
an = 6000 (1 +0.06
4)
π
, π = 1, 2, 3, β¦
Find the balance in the account after 5 years. (Hint: How many quarters are in 5 years?)
Learning Targets 1-6 Unit 6: Sequences and Summation Notation Practice 10.1
Unit 6 Practice Page 3
Expand and evaluate each sum.
18. β 5π =
6
π=1
19. β 2π2 =
4
π=1
20. β π(π + 4) =
5
π=1
21. β (β1
2)
π
=
4
π=1
22. β 11 =
9
π=5
23. β(β1)π
π!=
4
π=0
24. βπ!
(π β 1)!=
5
π=1
25. β(β1)π+1
(π + 1)!=
4
π=0
Learning Targets 1-6 Unit 6: Sequences and Summation Notation Practice 10.1
Unit 6 Practice Page 4
Express each sum using summation notation. Use 1 as the lower limit and i for the index of summation.
26. 12 + 22 + 32 + β― + 152 27. 2 + 22 + 23 + β― + 211
28. 1 + 2 + 3 + β― + 30 29. 1
2+
2
3+
3
4+ β― +
14
14+1
30. 4 + 42
2+
43
3+ β― +
4π
π 31. 1 + 3 + 5 β¦ + (2π β 1)
Express each sum using summation notation. Use a lower limit of summation and index of summation of your
choice.
32. 5 + 7 + 9 + 11 β¦ + 31 33. π + ππ + ππ2 + β― + ππ12
34. 6 + 9 + 12 + 15 β¦ + 33
35. (π + π) + (π + π2) + (π + π3) + (π + π4) + β― + (π + ππ)
Learning Targets 7-10 Unit 6: Arithmetic Sequences Practice 10.2
Unit 6 Practice Page 5
Write the first five terms of each arithmetic sequence.
1. π1 = 300 and π = β90 2. π1 =5
2 and π = β
1
2
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
3. ππ = ππβ1 + 6 if π1 = β9 4. ππ = ππβ1 +1
2 if π1 = β1
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Find the indicated term of the arithmetic sequence.
5. π1 = 13 and π = 4 π6 = ________ 6. π1 = 7 and π = 5 π50 = ________
7. π5 = β40 and π15 = β50 π200 = ________ 8. π20 = 35 and π = β3 π60 = ________
9. π16 = β60 and π40 = β48 π150 = ________ 10. π12 = β32 and π = 4 π70 = _______
11. π5 = 12 and π50 = 147 π92 = __________ 12. π7 = 10 and π = 0.5 π70 = _______
Learning Targets 7-10 Unit 6: Arithmetic Sequences Practice 10.2
Unit 6 Practice Page 6
Write a formula for the general term of each arithmetic sequence. Do not use a recursive formula. Then find the
20th
term of the sequence.
13. 1, 5, 9, 13, β¦ 14. 7, 3, -1, -5, β¦
ππ = ___________________ π20 = __________ ππ = ___________________ π20 = ________
15. π5 = 9 and π = 2 16. π12 = β20 and π = β4
ππ = ___________________ π20 = __________ ππ = ___________________ π20 = ________
17. ππ = ππβ1 + 3 if π1 = 4 18. ππ = ππβ1 β 10 if π1 = 30
ππ = ___________________ π20 = __________ ππ = ___________________ π20 = ________
19. In 1970, the median age of first marriage for U.S. men was 23.2. On average, this age has increased by
approximately 0.12 per year.
a. Write a formula for the nth term of the arithmetic sequence that describes the median age of first marriage for
U.S. men n years after 1969.
b. What will be the median age of the first marriage for U.S. men in 2009?
Learning Targets 7-10 Unit 6: Arithmetic Sequences Practice 10.2
Unit 6 Practice Page 7
Find the following sums.
20. The first 20 terms of the arithmetic sequence: 4, 10, 16, 22, . . . Sum = __________
21. The first 50 terms of the arithmetic sequence: β10, β6, β2, 2 . . . Sum = __________
22. The first 100 natural numbers. (Hint: 1, 2, 3, 4, . . ., 100) Sum = __________
23. The first 60 positive even integers. Sum = __________
24. The even integers between 21 and 45. Sum = __________
25. β(5π + 3) =
17
π=1
26. β(β3π + 5) =
30
π=1
Sum = __________ Sum = __________
27. β 4π =
100
π=1
28. β(1
2π β 5) =
42
π=0
Sum = __________ Sum = __________
Learning Targets 7-10 Unit 6: Arithmetic Sequences Practice 10.2
Unit 6 Practice Page 8
29. Mrs. Biberdorf wants to know how many people can sit in her churchβs pews.
The first row holds 4 people, the second row holds 7 people, the third row holds 10 people and so on. Her
church has 25 rows of pews.
How many people can sit in her churchβs pews?
30. Mrs. Neal is organizing cupcakes into the shape of a Christmas tree. She wants to top row to have one
cupcake, the second row to have two cupcakes, the third row to have three cupcakes, and so on. She wants the
final Christmas tree to have a total of 12 rows. How many cupcakes must she bake?
Learning Targets 1-10 Unit 6: Arithmetic Sequences Review Ch. 10.1 & 10.2 Set 1
Unit 6 Practice Page 9
Write the first four terms of the sequence
1. ππ = (β4)π 2. ππ =π!
π3
_____ _____ _____ _____ _____ _____ _____ _____
3. ππ = 4ππβ1 β π ππ π1 = 1
_____ _____ _____ _____
Simplify the ratio of factorials. Show your work.
4. 32!
29! ________________ 5.
π!
(πβ2)! ________________
Find the general formula for each sequence.
6. 1, 5, 9, 13, 17, . . . ππ = _________________
7. 3,3
8,
3
27 ,
3
64 ,
3
125 , β¦ ππ = _________________
8. 2, β4, 6, β8, 10, . . . ππ = _________________
9. 2
7,
5
7 ,
10
7 ,
17
7 ,
26
7, β¦ ππ = _________________
10. π1 = 5 πππ π = 3 ππ = _________________
11. π4 = 9 πππ π10 = β15 ππ = _________________
Learning Targets 1-10 Unit 6: Arithmetic Sequences Review Ch. 10.1 & 10.2 Set 1
Unit 6 Practice Page 10
Find the sum.
12. β(π2 β 2) = _________________
7
π=3
13. β 8 =
3
π=1
_________________
14. β (1
π!) = _________________
4
π=2
15. β(β2π + 6) =
25
π=1
_________________
16. The first 22 terms of the arithmetic sequence 5, 12, 19, 26β¦ _______________
Use summation notation (sigma notation) to write the following sums.
17. 1 + 3 + 5 + 7 + β¦ + [2(12) - 1] _______________
18. [3 + (1
3)
2] + [3 + (
1
4)
2] + [3 + (
1
5)
2] + β― + [3 + (
1
9)
2] _______________
19. 1 β 2 + 4 β 8 + 16 β 32 + 64 β 128 _______________
20. 3
2+
9
4+
27
8+
81
16+
243
32 _______________
21. 3 + 8 + 15 + 24 + 35 _______________
Learning Targets 1-10 Unit 6: Arithmetic Sequences Review Ch. 10.1 & 10.2 Set 2
Unit 6 Practice Page 11
Write the first five terms of the sequence
1. ππ = π2 + 1 2. ππ =π2
π!
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
3. ππ = 3ππβ1 β π ππ π1 = 1 4. ππ = π! β 1
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Simplify the ratio of factorials. Show your work.
5. 43!
47! __________ 6.
(π+1)!
(πβ1)! __________
Find the general formula for each sequence.
7. π =1
3 πππ π1 =
1
3 ππ = _________________
8. 0,7
3,
26
3 ,
63
3 , β¦ ππ = _________________
9. β5, 10, β15, 20, . . . ππ = _________________
10. π = β9 πππ π1 = 33 ππ = _________________
11. π5 = 129 πππ π17 = β15 ππ = _________________
Learning Targets 1-10 Unit 6: Arithmetic Sequences Review Ch. 10.1 & 10.2 Set 2
Unit 6 Practice Page 12
Find the sum.
12. β(7π + 5) = _________________
10
π=0
13. β 5 =
21
π=1
_________________
14. β(π! + 4) = _________________
5
π=1
15. β π =
18
π=1
_________________
16. The first 25 terms of the arithmetic sequence 3, 6, 9, 12, β¦ _______________
Use summation notation (sigma notation) to write the following sums.
17. 15 + 18 + 21 + 24 + β¦ + 54 _______________
18. [5 +1
2] + [5 +
2
9] + [5 +
2
16] + β― + [5 +
2
81] _______________
19. β 2 + 6 β 10 + 14 β 18 _______________
20. Find the seating capacity of an auditorium with 30 rows of seats if there are 20 seats in the first row, 27 seats in
the second row, 34 seats in the third row and so on.
_______________
Learning Targets 1-10 Unit 6: Arithmetic Sequences Review Ch. 10.1 & 10.2 Set 3
Unit 6 Practice Page 13
Write the first five terms of the sequence
1. ππ =(β1)π
2π2 2. ππ =π!
3πβ1
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
3. ππ = ππβ1(π + 2) ππ π1 = 4
_____ _____ _____ _____ _____
Simplify the ratio of factorials. Show your work.
4. 12!
9! ____________ 5.
(π+3)!
(π+1)! ____________
Find the general formula for each sequence.
6. 2, 4, 8, 16, 32, . . . ππ = _________________
7. β1
3,
1
9 , β
1
27 ,
1
81 , β¦ ππ = _________________
8. 10, 3, β4, β11, . . . ππ = _________________
9. ππ = ππβ1 + 3 ππ π1 = 4 ππ = _________________
Find the sum.
10. β1
π2 = _________________
4
π=1
11. β2π
π + 1=
3
π=0
_________________
Learning Targets 1-10 Unit 6: Arithmetic Sequences Review Ch. 10.1 & 10.2 Set 3
Unit 6 Practice Page 14
12. β(3π + 4) = _________________
30
π=1
13. βπ + 5
3=
14
π=0
_________________
14. The first 40 terms of the arithmetic sequence 7, 10, 13, 16β¦ _______________
15. The first 40 terms of the arithmetic sequence with π1 = 10 and π12 = 32. _______________
Use summation notation (sigma notation) to write the following sums.
16. 1
4β
1
8+
1
16β
1
32+
1
64 _______________
17. 1
1+
1
4+
2
16+
6
64+
24
256 _______________
Using the given information for an arithmetic sequence, find the missing value.
18. π6 = 21 πππ π = 4 19. π4 = 8 πππ π12 = 12
π20 = ____________ π22 = ____________
20. π5 = 10 πππ π = 3 21. π5 = 8.5 πππ π12 = 19
π25 = ____________ π9 = ____________
Learning Targets 11-15 Unit 6: Geometric Sequences Practice 10.3
Unit 6 Practice Page 15
Write the first five terms of each geometric sequence.
1. π1 = 5 πππ π = 3 2. π1 = 20 πππ π =1
2
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
3. ππ = β4ππβ1 ππ π1 = 10 4. ππ = β5ππβ1 ππ π1 = β6
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
5. ππ = β3ππβ1 ππ π1 = 10
_____ _____ _____ _____ _____
Use the formula for the general term of a geometric sequence to find the indicated term.
6. π1 = 6 πππ π = 2 7. π1 =1
4 πππ π5 = 4
π8 = ____________ π12 = ____________
8. π2 = 10 πππ π5 = 0.01 9. π3 =2
3 πππ π5 =
2
27
π8 = ____________ π8 = ____________
10. π1 = 4 πππ π = β2 11. 3, 15, 75, 375, β¦
π12 = ____________ π7 = ___________
Learning Targets 11-15 Unit 6: Geometric Sequences Practice 10.3
Unit 6 Practice Page 16
Write a general formula for each geometric sequence. Use the formula to find π7 (the 7th
term).
12. 3, 12, 48, 192, β¦ 13. 18, 6, 2,2
3, β¦
ππ = _____________________ π7 = __________ ππ = _____________________ π7 = __________
14. 1.5, β3, 6, β12, β¦ 15. 0.0004, β0.004, 0.04, 0.04, β0.4 β¦
ππ = _____________________ π7 = __________ ππ = _____________________ π7 = __________
16. Suppose you save $1 on the first day of a month, $2 the second day, $4 the third day, and so on. That is, each
day you save twice as much as you did the day before. What will you put aside on the fifteen day of the month?
17. A professional baseball player signs a contract with a beginning salary of $3,000,000 for the first year and an
annual increase of 4% per year beginning in the second year. That is, beginning in year 2, the athleteβs salary will
be 1.04 times what it was in the previous year. What is the athleteβs salary for year 7 of the contract?
Learning Targets 11-15 Unit 6: Geometric Sequences Practice 10.3
Unit 6 Practice Page 17
Find the sums.
18. First 12 terms of 2, 6, 18, 54, . . . 19. First 11 terms of 3, β6, 12, β24, . . .
Sum = __________ Sum = __________
20. First 14 terms of β3
2, 3, β6, 12 β¦ 21. β(3)π =
8
π=1
Sum = __________ Sum = __________
22. β 5 β 2π =
10
π=1
23. β (1
2)
π+1
=
6
π=1
Sum = __________ Sum = __________
Find the sum of each infinite geometric series.
24. 1 + 1
3+
1
9+
1
27+ β― 25. 3 +
3
4+
3
42 +3
43 + β―
Sum = __________ Sum = __________
Learning Targets 11-15 Unit 6: Geometric Sequences Practice 10.3
Unit 6 Practice Page 18
26. 1 β1
2+
1
4, β
1
8+ β― 27. β 8(β0.3)πβ1
β
π=1
Sum = __________ Sum = __________
The general term of a sequence is given. Determine whether the sequence is arithmetic, geometric or neither. If it
is arithmetic, state the common difference. If it is geometric, state the common ratio.
28. ππ = π + 5 29. ππ = 2π 30. ππ = π2 + 5
Use the formula for the value of an annuity to solve. Hint: π΄ =π[(1+
π
π)
ππ‘β1]
π
π
P is the deposit made at the end of each compounding period
r is the percent interest compounded n times per year
A is the value of the annuity after t years
31. To save for retirement, you decide to deposit $2500 into an IRA at the end of each year for the next 40 years.
If the interest rate is 9% per year compounded annually, find the value of the IRA after 40 years.
32. You decide to deposit $100 at the end of each month into an account paying 8% interest compounded
monthly to save for your childβs education. How much will you save over 16 years?
Learning Targets 1-15 Unit 6: Sequences & Series Review 10.1-10.3 Set 1
Unit 6 Practice Page 19
Find the first five terms of each sequence.
1. ππ = (β1)π (π
π+2) 2. ππ = ππβ1 + 3π ππ π1 = 6
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
Write an expression for the most apparent nth term of the sequence.
3. 1
3, β
1
6,
1
9, β
1
12,
1
15, β¦ ππ=
Use sigma notation to write the given sum.
4. 1
4+
2
8+
3
16+ β― +
6
128 _________________________
Using the given information for an ARITHMETIC sequence to find the missing value.
5. π4 = β10 πππ π = 4 π12 = ________ 6. π6 = 18 πππ π10 = β6 π15 =________
7. Find the sum of the first 15 terms of the arithmetic sequence if π1 = 4 πππ π15 = 88.
S = __________
Use the given information for a GEOMETRIC sequence to find the missing value.
8. π1 = 2 πππ π = 1.1 π8 = _______ 9. π4 = 3 πππ π9 =1024
81 π1 = ______
Learning Targets 1-15 Unit 6: Sequences & Series Review 10.1-10.3 Set 1
Unit 6 Practice Page 20
Find the sum. (HINT: First determine if the sequence is arithmetic, geometric or infinite geometric.)
10. First 20 terms of 8 + 11 + 14 + 17 + β¦ 11. First 15 terms of 2 + 6 + 18 + 54 + β¦
S = ____________ S = ____________
12. β 3 (3
2)
π
=
500
π=1
13. β(2π β 1) =
100
π=0
S = ____________ S = ____________
14. β4
π!=
3
π=0
15. βπ2
3π + 2=
6
π=2
S = ____________ S = ____________
16. β 2 (1
2)
π
=
β
π=1
17. 4 β 1 +1
4β
1
16+ β―
S = ____________ S = ____________
Learning Targets 1-15 Unit 6: Sequences & Series Review 10.1-10.3 Set 2
Unit 6 Practice Page 21
Write the first five terms of each sequence.
1. ππ = β1
4ππβ1 ππ π1 = 4 2. ππ =
2π
π2
______ ______ ______ ______ ______ ______ ______ ______ ______ ______
Simplify.
3. (π+2)!
(πβ1)! _______________ 4.
82!
85! _______________
Write an expression for the most apparent nth term of these sequences.
5. 3
2,
5
4,
7
6,
9
8,
11
10, β¦ ππ=
6. 1, 2, 4, 8, β¦ ππ=
7. 1, β1, β3, β5, β¦ ππ=
Find the sum of these sequences.
8. The first 18 terms of 1, β3, β7, β11, β¦ 9. The first 8 terms of 3 + 1 +1
3+
1
9+ β―
S = ______________ S = ______________
10. β 4 (1
2)
πβ1β
π=1
S = ______________
Learning Targets 16-19 Unit 6: Binomial Theorem Practice 10.5
Unit 6 Practice Page 22
Evaluate each binomial coefficient.
1. (83) = _____ 2. (12
1) = _____ 3. (6
6) = _____ 4. (100
2) = _____
Use the Binomial Theorem to expand each binomial and express in simplified form.
5. (π₯ + 2)3 = ________________________________________
6. (5π₯ β 1)3 = ________________________________________
7. (π₯2 + 2π¦)4 = ________________________________________
8. (2π₯3 β 1)4 = ________________________________________
Learning Targets 16-19 Unit 6: Binomial Theorem Practice 10.5
Unit 6 Practice Page 23
Use the Binomial Theorem to expand each binomial. Express the result in simplified form.
9. (3π₯ + π¦)3 10. (π¦ β 3)4
__________________________________ __________________________________
Write the first three terms in each binomial expansion. Express the result in simplified form.
11. (π₯ + 2)8 12. (π₯2 + 1)16
__________________________________ __________________________________
Find the term indicated in each expansion.
13. (2π₯ + π¦)6 Third term__________ 14. (π₯2 β π¦3)8 Sixth term__________
15. (π₯2 + π¦)22 π¦14 term __________ 16. (π₯2 β 2π¦)12 π₯8 term __________
Learning Targets 16-19 Unit 6: Binomial Theorem More Practice 10.5
Unit 6 Practice Page 24
Expand each binomial. Simplify.
1. (3π₯ + 2)3 _______________________________________________________
2. (2π₯ + 7)5 _______________________________________________________
3. (4π₯ β π¦)4 _______________________________________________________
4. Find the coefficient of π₯3 in the expansion of (π₯ + 2)8. _________________
5. Find the coefficient of π₯6 in the expansion of (2π₯ β 3)14. _________________
6. Find the coefficient of π₯3π¦6 in the expansion of (π₯ β 6π¦)9. _________________
7. Find the coefficient of π₯5π¦7 in the expansion of (3π₯ + 4)12. _________________
Learning Targets 1-19 Unit 6: Sequences and Series Practice Test
Unit 6 Practice Page 25
Write the first four terms of each sequence.
1. ππ = (β3)π __________ __________ __________ __________
2. ππ = 2ππβ1 β 5 ππ π1 = 2 __________ __________ __________ __________
Simplify each ratio of factorials. Leave answers as fractions (not decimals) if possible.
3. 18!
20! _______________ 4.
(3π+1)!
(3πβ1)! _______________
Write an expression for the most apparent nth term.
5. 3, β6, 9, β12, 15 6. 4, 9, 14, 19, 24
ππ= ππ=
Find each sum.
7. β 3 = _________________
5
π=1
8. β(3 β 4π) =
3
π=0
_________________
Use sigma notation to write the sum.
9. [2 + (1
2)
2] + [2 + (
2
3)
2] + [2 + (
3
4)
2] + β― + [2 + (
9
10)
2] ______________________
10. 2
8+
2
27+
2
64+ β― +
2
343 ______________________
Learning Targets 1-19 Unit 6: Sequences and Series Practice Test
Unit 6 Practice Page 26
Using the given information for an arithmetic sequence, find the missing value.
11. π1 = 4 πππ π =1
3 12. π3 = 1.25 πππ π7 = β3.15
π13 = _________________ π10 = _________________
13. Find the sum of the first 15 terms of the arithmetic sequence given π1 = 4 πππ π15 = 88.
S = _________________
Using the given information for a geometric sequence, find the missing value.
14. π1 = 2 πππ π = 1.1 15. π4 = 3 πππ π9 =1024
81
π8 = _________________ π1 = _________________
Find each sum. (Hint β determine whether the sequence is arithmetic or geometric, first)
16. The first 20 terms of 8 + 11 + 14 + 17 + β― 17. β 3 (1
3)
π
=
40
π=1
S = _________________ S = _________________
18. The first 15 terms of 2 + 6 + 18 + 54 + β― 19. β(6π β 4) =
250
π=0
S = _________________ S = _________________
Learning Targets 1-19 Unit 6: Sequences and Series Practice Test
Unit 6 Practice Page 27
20. Find the sum of the infinite geometric series: 4 β 1 +1
4β
1
16+ β― S = ________________
21. Determine the seating capacity of an auditorium with 36 rows of seats if there are 16 seats in the first row, 18
seats in the second row, 20 seats in the third row, and so on.
S = _________________
22. Evaluate: (4038
) = ___________
Expand each binomial. Simplify.
23. (π₯ + 2π¦)5 _______________________________________________________
24. (2 β 3π)4 _______________________________________________________
25. Find the 4th
term in the expansion of (π₯
2+ 3)
8. ____________________
Learning Targets 1-19 Unit 6: Sequences and Series Practice Test
Unit 6 Practice Page 28
Find the coefficient of the given term in the expansion of each binomial.
26. the π₯5π¦7 term of (π₯ + 5π¦)12 ____________________
27. the π₯4 term of (3π₯ β 2)11 ___________________
28. the π₯8 term of (π₯2 + 4)6 ____________________
Learning Targets 1-19 Unit 6: Sequences and Series Extra Review
Unit 6 Practice Page 29
1. Find the 1st
term of the arithmetic sequence with π16 = 22 πππ π10 = 72. __________________
2. Find the 10th
term of the geometric sequence with π2 = 3 πππ π5 =3
64. __________________
3. Find the 30th
term of this sequence: 5, 2, β1, β4, . . . __________________
4. Find the 20th
term of this sequence: 4, 10, 25, 62.5, . . . __________________
Find each sum.
5. β 4 (4
3)
π
= _________________
13
π=0
6. β3π + 1
4=
25
π=1
_______________ 7. β(2π2 β 1) =
4
π=0
___________
8. Find the sum of the infinite geometric series: 3 β 1 +1
3β
1
9+ β― S = _____________
Learning Targets 1-19 Unit 6: Sequences and Series Extra Review
Unit 6 Practice Page 30
Find the coefficient of the given term in the expansion of each binomial.
9. the π₯2π¦8 term of (4π₯ β π¦)10 ____________________
10. the π₯10 term of (π₯2 β 3)8 _____________________
11. Find the 8th
term in the expansion of (2π₯ β 3)14. _____________________
12. Find the 6th
term in the expansion of (4π₯ + 1)10. _____________________
13. Expand and simplify: (π₯ β 2π¦)5 ___________________________________________________
Write a formula for the most apparent nth term. Remember, n must start with 1.
14. 1
1, β
8
2,
27
3, β
64
4, β¦ 15. 4, 9, 16, 25, . . .
____________________ ____________________
Recommended