Objective: The student will recognize arithmetic sequences, extend and write formulas for arithmetic sequences. S. Calahan 2008 Arithmetic Sequences 4-7

vocabulary Sequence – 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, This is not an arithmetic sequence because the difference between terms is not constant.

Arithmetic Sequence Since this sequence has a common difference it is an arithmetic sequence.

Writing arithmetic sequences An arithmetic sequence can be found as follows a 1, a 1 +d, a 2 +d, a 3 +d,… ? ? ? The common difference is -7

? ? ? Add -7 to the last term of the sequence to find the next three terms. 53, 46, 39, 32

n th term of an Arithmetic Sequence The n th term of an arithmetic sequence with first term a 1 and common difference d is given by a n = a 1 + (n – 1)d, where n is a positive integer.

Find a specific term Find the 14 th term in the arithmetic sequence 9, 17, 25, 33,… The common difference is +8 Use the formula for the n th term a n = a 1 + (n – 1) d a 1 = 9, n = 14, d = 8 a 14 = 9 + (14 – 1)8 = = 113

Write and equation for a squence Write an equation for the n th term of the squence, 12, 23, 34, 45, … a n = a 1 + (n – 1)d a 1 = 12, d = 11 a n = 12 + (n -1)11 a n = n – 11 Distributive property a n = 11n + 1

Use the equation to solve for the 10 th term a n = 11n + 1 n = 10 a 10 = 11(10) + 1 replace n with 10 a 10 = 111