Question

What is the recursive and explicit formula of the geometric sequence?

2,5, 12.5, 31.25, 78, 125, ...

Answer 1

Option (2)

Explanation:

Given geometric sequence is,

2, 5, 12.5, 31.25, 78.125......

First term = a₁ = 2

Common ratio of the sequence = r =
`(5)/(2)`

= 2.5

Recursive formula of a geometric sequence is given by,

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

Here,
`a_n=` nth term of the sequence

`a_(n-1)=` (n - 1)th term

r = common ratio

Therefore, recursive formula for the given sequence will be,

`a_1=2`

`a_n=a_(n-1)(2.5)`

Explicit formula of a geometric sequence is given by,

`a_n=a_1(r)^(n-1)`

Therefore, explicit formula of the sequence will be,

`a_n=2(2.5)^(n-1)`

Option (2) will be the correct option.