12.2 Arithmetic Sequences ©2001 by R. Villar All Rights Reserved

Arithmetic Sequences Arithmetic Sequence: sequence whose consecutive terms have a common difference. Example: 3, 5, 7, 9, 11, 13,... The terms have a common difference of 2. The common difference is the number d. Example: Is the sequence arithmetic? –45, –30, –15, 0, 15, 30 Yes, the common difference is 15 How do you find any term in this sequence? To find any term in an arithmetic sequence, use the formulaa n = a 1 + (n – 1)d where d is the common difference.

Example: Find a formula for the nth term of the arithmetic sequence in which the common difference is 5 and the first term is 3. a n = a 1 + (n – 1)d a 1 = 3 d = 5 a n = 3 + (n – 1)5

Example: If the common difference is 4 and the fifth term is 15, what is the 10th term of an arithmetic sequence? a n = a 1 + (n – 1)d We need to determine what the first term is... d = 4 and a 5 = 15 a 5 = a 1 + (5 – 1)4 = 15 a 1 = –1 a 10 = –1 + (10 – 1)4 a 10 = 35

Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence. A. 12, 8, 4, 0, … B. 1, 4, 9, 16, …

Find the indicated term of each arithmetic sequence. A. 22nd term: 5, 2, -1, -4, … B. 15th term: a1 = 7; d = 3

a. Find the next three terms of the arithmetic sequence 0, 9, 18, 27,… b. Find the 7th term of the arithmetic sequence 10, 23, 36,...

Which of the following is the 24th term of the arithmetic sequence 3, 2, 7, 12,...? A 62 B 92 C 112 D 162

100 Category 1 Answer 3, 6, 9, ___, ___,___

Answer 100 Category 1 3, 6, 9, 12, 15, 18

200 Category 1 Answer 20, 12, 4, ___, ___,___

Answer 200 Category 1 20, 12, 4, -4, -12, -20

300 Category 1 Answer 800, 400, 200,, ___, ___,___

Answer 300 Category 1 800, 400, 200, 100, 50,25

400 Category 1 Answer 3, 5, 8, 12, ___, ___,___

Answer 400 Category 1 3, 5, 8, 12, 17, 23,30

500 Category 1 Answer 1,1,2,3,5,8, ___, ___,___

Answer 500 Category 1 1,1,2,3,5,8, 13, 21,34

100 Category 2 Answer Write the rule if a 1 = 10 d = 3

Answer 100 Category 2 Write the rule if a 1 = 10 d = 3 a n = 7 + 3n

200 Category 2 Answer Write the rule if a 3 = 15 d = -2

Answer 200 Category 2 Write the rule if a 3 = 15 d = -2 a n = n

300 Category 2 Answer Write the first 5 terms for a n =6+5n

Answer 300 Category 2 Write the first 5 terms for a n =6+5n 11, 16, 21, 26, 31

400 Category 2 Answer Find a 20 for 10, 6, 2, -2...

Answer 400 Category 2 Find a 20 for 10, 6, 2, -2… a n =14 - 4n so a 20 = (20) = -66

500 Category 2 Answer Find the rule if a 3 = 5 and a 7 = 9

Answer 500 Category 2 Find the rule if a 3 = 5 and a 7 = 9 __,__,5,__,__,__,9 d = (9-5)/(7-3) =1 a n = 2 +1n