The question is in the image below.

The Recursive Formula for the sequence is:

    ; a₁ = 125

Hence, option D is correct.

Step-by-step explanation:

We know that a geometric sequence has a constant ratio 'r'.

The formula for the nth term of the geometric sequence is

where

aₙ is the nth term of the sequence

a₁ is the first term of the sequence

r is the common ratio

We are given the explicit formula for the geometric sequence such as:

comparing with the nth term of the sequence, we get

a₁ = 125

r = 1/5

Recursive Formula:

We already know that

We know that each successive term in the geometric sequence is 'r' times the previous term where 'r' is the common ratio.

i.e.

Thus, substituting r = 1/5

and a₁ = 125.

Therefore, the Recursive Formula for the sequence is:

    ; a₁ = 125

Hence, option D is correct.

a. is correct