Question

An arithmetic sequence is represented by the explicit formula A(n) = 2 + 9(n - 1). What is the recursive formula?. . A. A(n) = A(n - 1) + 2. . B. A(n) = A(n - 1) + 9. . C. A(n) = A(n - 1) - 9. . D. A(n) = A(n - 1) - 3

Answer 1

A(n) = 2 + 9(n - 1) = 2 + 9n - 9
A(n + 1) = 2 + 9(n + 1 - 1) = 2 + 9n = (2 + 9n - 9) + 9 = A(n) + 9

Therefore, the recursive formular is A(n) = A(n - 1) + 9

Answer 2

The first term of a sequence:
A 1 = 2 + 9 ( 1 - 1 ) = 2
The 2nd term of a sequence:
A 2 = 2 + 9 ( 2 - 1 ) = 2 + 9 = 11
The common difference is:
d = A2 - A1 = 11-2 = 9
The recursive formula is:
B ) A (n) = A(n-1) +9