Question

What is the recursive and explicit formula of the geometric sequence?
2,5, 12.5, 31.25, 78, 125, ...

Answer 1

Answer:

Option (2)

Step-by-step explanation:

Given geometric sequence is,

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

First term = a₁ = 2

Common ratio of the sequence = r = $\frac{5}{2}$

                                                          = 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.