Question

Please help. . . . . . . . .

Answer 1

9514 1404 393

Answer:

  recursive: 5, 3, 2

  explicit: 5, 3

Step-by-step explanation:

First of all, you can identify the first term as a1 = 5.

Then you can see that the ratio of consecutive terms is ...

  15/5 = 45/15 = 135/45 = 405/135 = 3 . . . the common ratio

In the recursive formula, a1 is the first term (5), and the multiplier getting you to the next term is the common ratio (3). The recursion relation is good for values of n such that n-1 is at least 1. That is, n ≥ 2.

  $\text{The recursive rule is }a_1=\boxed{5}\text{ and }a_n=\boxed{3}a_{n-1}\text{ for }n\ge\boxed{2}$

__

The explicit rule is formed the way the problem statement tells you: the first term times a power of the common ratio.

  $\text{The explicit rule is }a_n=\boxed{5}(\boxed{3})^{n-1}$