Question

A geometric sequence is defined recursively by an=5an-1. The 1st term of the sequence is 0.45. Which of the following is the explicit formula for the nth term of sequence?

Answer 1

`a_(n)` = 0.45
`(5)^(n-1)`

Explanation:

the n th term of a geometric sequence is

`a_(n)` =
`a_(1)`
`(r)^(n-1)`

where r is the common ratio and
`a_(1)` the first term

here
`a_(1)` = 0.45 and r = 5, hence

`a_(n)` = 0.45
`(5)^(n-1)` ← explicit formula