Holt Algebra 1

4-6 Arithmetic Sequences

9 3 12x

Solve the compound inequality and graph the solutions.

8 < 3x – 1 ≤ 11

3 < x ≤ 4–5 –4 –3 –2 –1 0 1 2 3 4 5

11 1

33 3

Holt Algebra 1

4-6 Arithmetic Sequences

Recognize and extend an arithmetic sequence.Find a given term of an arithmetic sequence.

Objectives

Holt Algebra 1

4-6 Arithmetic Sequences

During a thunderstorm, you can estimate your distance from a lightning strike by counting the number of seconds from the time you see the lightning until you hear the thunder. When you list the times and distances in order, each list forms a sequence.

A sequence is a list of numbers that often forms a pattern. Each number in a sequence is a term.

Holt Algebra 1

4-6 Arithmetic Sequences

Distance (mi)

1 542 6 7 83

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Time (s)

+0.2 +0.2 +0.2 +0.2+0.2+0.2 +0.2

When the terms of a sequence differ by the same nonzero number d, the sequence is an arithmetic sequence and d is the common difference.

Time (s)

Distance (mi)

Holt Algebra 1

4-6 Arithmetic Sequences

Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms.

9, 13, 17, 21,…

+4 +4 +4

4d 9, 13, 17, 21 25, 2, 9, 33

is an arithmetic sequence

Holt Algebra 1

4-6 Arithmetic Sequences

Reading Math

The three dots at the end of a sequence are called an ellipsis. They mean that the sequence continues and can read as “and so on.”

Holt Algebra 1

4-6 Arithmetic Sequences

Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms.

10, 8, 5, 1,…-2 -3 -4

is not an arithmetic sequence

Holt Algebra 1

4-6 Arithmetic Sequences

Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms.

+1/2 +1/2 +1/212

d

3 1 1 3, , , ,4 4 4 4

1 3 1 1 , 1 , 24 4 4

is an arithmetic sequence

Holt Algebra 1

4-6 Arithmetic SequencesThe variable a is often used to represent terms in a sequence. The variable a9, read “a sub 9,” is the ninth term, in a sequence. To designate any term, or the nth term in a sequence, you write an, where n can be any number.

1 2 3 4… n Position

The sequence above starts with 3. The common difference d is 2. You can use the first term and the common difference to write a rule for finding an.

3, 5, 7, 9… Terma1 a2 a3 a4 an

Holt Algebra 1

4-6 Arithmetic Sequences

1

Arithmetic Sequence1na a n d

Holt Algebra 1

4-6 Arithmetic SequencesFind the 16th term of the arithmetic sequence.4, 8, 12, 16, …

1 1na a n d 4 1 4na n 16 4 16 1 4a 4 15 4

4 64

06

Holt Algebra 1

4-6 Arithmetic SequencesFind the 25th term of the arithmetic sequence.a1 = –5; d = –2

1 1na a n d

5 1 2na n

25 5 25 1 2a 5 24 2

5 4853

Holt Algebra 1

4-6 Arithmetic SequencesFind the 12th term of the arithmetic sequence.

a1 = 4.2; d = 1.4

1 1na a n d

4.2 1 1.4na n

12 4.2 12 1 1.4a 4.2 11 1.4

4.2 15.419.6

Holt Algebra 1

4-6 Arithmetic SequencesEach time a truck stops, it drops off 250 pounds of cargo. It started with a load of 2000 pounds. How much does the load weigh after the 5th stop?

HW pp. 275-277/10,12,15-53 odd

-250 -250-250 -250 -250

2000 1750 1500 1250 1000 750

750 lbs

2000 1 250na n 1 1na a n d

6 2000 6 1 250a

1a