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Objective: The student will recognize arithmetic sequences, extend and write formulas for arithmetic sequences.

S. Calahan

2008

Arithmetic Sequences 4-7

vocabularySequence – a set of numbers in a specific order.

Terms – the numbers in the sequence

Arithmetic sequence – if the difference between successive terms is constant.

Common difference – the difference between the terms

Identify Arithmetic Sequences

• Determine whether the sequence is arithmetic.

1, 2, 4, 8, . . . +1 +2 +4

This is not an arithmetic sequence because the difference between terms is not constant.

Arithmetic Sequence

7 12 17 22 27

+5 +5 +5 +5

Since this sequence has a

common difference it is an

arithmetic sequence.

Writing arithmetic sequences

• An arithmetic sequence can be found as follows

a1, a1+d, a2+d, a3+d,…

74 67 60 53 ? ? ? -7 -7 -7 -7 -7 -7

The common difference is -7

74 67 60 53 ? ? ?

• Add -7 to the last term of the sequence to find the next three terms.

53, 46, 39, 32

nth term of an Arithmetic Sequence

• The nth term of an arithmetic sequence with first term a1 and common difference d is given by

an = a1 + (n – 1)d, where n is a positive integer.

Find a specific term

• Find the 14th term in the arithmetic sequence 9, 17, 25, 33,…

• The common difference is +8

• Use the formula for the nth term

an = a1+ (n – 1) d a1 = 9, n = 14, d = 8

a14 = 9 + (14 – 1)8

= 9 + 104 = 113

Write and equation for a squence

• Write an equation for the nth term of the squence, 12, 23, 34, 45, …

an = a1 + (n – 1)d a1 = 12, d = 11

an = 12 + (n -1)11

an = 12 + 11n – 11 Distributive property

an = 11n + 1

Use the equation to solve for the 10th term

an = 11n + 1 n = 10

a10 = 11(10) + 1 replace n with 10

a10 = 111