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

2. 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

3. 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.

4. Arithmetic Sequence 712 17 22 27 +5 +5 +5 +5 Since this sequence has a common difference it is an arithmetic sequence.

5. Writing arithmetic sequences An arithmetic sequence can be found as follows a 1, a 1 +d, a 2 +d, a 3 +d,… 74 67 60 53 ? ? ? -7 -7 -7 -7 -7 -7 The common difference is -7

6. 74 67 60 53 ? ? ? Add -7 to the last term of the sequence to find the next three terms. 53, 46, 39, 32

7. 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.

8. 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 = 9 + 104 = 113

9. 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 = 12 + 11n – 11 Distributive property a n = 11n + 1

10. 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