Name
6-2
Class
Date
Form K
Practice
Arithmetic Sequences in Recursive Form
Write a recursive formula for each arithmetic sequence below. What is the
value of the sixth term?
1. 15, 11, 7, 3, –1, . . .
2. –2, 2, 6, 10, 14, . . .
3. 1.5, 3, 4.5, 6, . . .
4. 6.8, 5.4, 4, 2.6, . . .
5. 1, 10, 19, 28, . . .
61. –27, –22, –17, –12, . . .
Use each recursive definition to find the first four terms of the arithmetic
sequence it defines.
7. A(n) = A(n – 1) + 6; A(1) = 9
8. A(n) = A(n – 1) + 4; A(1) = –10
9. A(n) = A(n – 1) + 15; A(1) = –9
10. 1 A(n) = A(n – 1) – 11; A(1) = 3
11. A(n) = A(n – 1) – 12; A(1) = 7
12. A(n) = A(n – 1) – 23.5; A(1) = 72
13. You budget $100 for parking each month. It costs you $5 each day you use the
downtown parking lot. How much money is left in your budget after you have used
the downtown parking lot 11 times this month?
14. You start an investment account with $3000 and save $100 each month. How
much money will you have invested after 12 months?
Pearson Texas Algebra I
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name
6-2
Class
Date
Form K
Practice (continued)
Arithmetic Sequences in Recursive Form
Write a recursive definition for each explicit formula.
15. A(n) = 6 + (n – 1)( –2)
16. A(n) = 12 + (n – 1)(5)
17. A(n) = –2.2 + (n – 1)( –1)
18. A(n) = 5 + (n – 1)(0.5)
19. A(n) = –3 + (n – 1)(6)
20. A(n) = –7.6 + (n – 1)(3)
Write an explicit formula for each recursive formula.
21. A(n) = A(n – 1) – 6; A(1) = 22
22. A(n) = A(n – 1) + 3; A(1) = 19
23. A(n) = A(n – 1) + 9; A(1) = –18
24. A(n) = A(n – 1) + 0.6; A(1) = 1.5
25. Open-Ended Write an explicit formula for the arithmetic sequence whose common
difference is –18.
26. Reasoning The initial term of an arithmetic sequence is 5. The eleventh term is 125.
What is the common difference of the arithmetic sequence?
27. Writing Explain how you can determine if a sequence is arithmetic.
Pearson Texas Algebra I
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.