Question

Given the explicit formula u(n) = -13 + 18n, where u(1) = 5, find the recursive formula for u(n).

A. u(1) = 5 and u(n + 1) = u(n) + 18, for n = 1, 2, 3, . . .
B. u(1) = 5 and u(n + 1) = 5u(n) + 18, for n = 1, 2, 3, . . .
C. u(1) = 5 and u(n + 1) = u(n) + 5, for n = 1, 2, 3, . . .
D. u(1) = 5 and u(n + 1) = 18u(n) + 5, for n = 1, 2, 3, . . .

Answer 1

The recursive formula for the sequence with the explicit formula u(n) = -13 + 18n is u(1) = 5 and u(n + 1) = u(n) + 18 for n = 1, 2, 3, ..., which corresponds to option A.

Step-by-step explanation:

The student is asking for the recursive formula for the sequence given by the explicit formula u(n) = -13 + 18n, where u(1) = 5. To find this recursive formula, we need to express u(n+1) in terms of u(n). Let's start with the explicit formula and find the value for u(n+1):

u(n+1) = -13 + 18(n+1)
= -13 + 18n + 18
= ( -13 + 18n) + 18
= u(n) + 18.

Thus, the recursive formula is:

u(1) = 5 and u(n + 1) = u(n) + 18, for n = 1, 2, 3, ...

Therefore, the correct answer is option A: u(1) = 5 and u(n + 1) = u(n) + 18, for n = 1, 2, 3, ...