12.1-12.3 Review – Algebra II Arithmetic Sequence a n = a 1 + (n – 1)d Arithmetic Series S n =n ( a 1 +a n 2 ) Geometric Sequence a n =a 1 ⋅ r n−1 Geometric Series S n = a 1 ( 1−r n ) 1−r Write the next term in the sequence. Then write a rule for the n th term. 1. 7, 11, 15, 19, … 2. -3, 6, -9, 12, … 3. 2 3 , 2 9 , 2 27 , 2 81 , ... Find the sum of the series. 4. ∑ n=1 5 n 2 5. ∑ i=2 7 ( 3 i−5 ) 6. ∑ k=1 5 k 5
Worksheet Review for chapters 12 and 13. No answers included.
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12.1-12.3 Review Algebra II
Arithmetic Sequence
an = a1 + (n 1)d
Arithmetic Series
Geometric Sequence
Geometric Series
Write the next term in the sequence. Then write a rule for the
nth term.
1.7, 11, 15, 19,
2.-3, 6, -9, 12,
3.
Find the sum of the series.
4.
5.
6.
Write a rule for the nth term an of the arithmetic or geometric
sequence. Find a8, then find the sum of the first 8 terms of the
sequence using the formula.
7.7, 10, 13, 16, .
8.5, 10, 20, 40, 80,
9.
10.3, 1, -1, -3, -5,
11.You are trying to find the maximum weight that you can lift
in a weightlifting exercise. You start with a single lift of 125
pounds. Then you increase the weight by 2 pounds and try again. You
repeat this procedure until you reach a weight that you are unable
to lift.
a.Write a rule for the total weight of your nth lifting
attempt.
b.You are unable to lift the weight on your sixth lift. So,
based on your fifth lift, what is the maximum amount of weight that
you can lift in this exercise?
c.Find the sum of the weights lifted in your five successful
lifts.
12.You invest $20,000 in a retirement plan. The plan is expected
to have an annual return of 12%. Write a rule for the amount of
money an available in the plan at the beginning of the nth year.
What is the balance of the account at the beginning of the 20th
year?
