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 = [tex]\frac{5}{2}[/tex]
= 2.5
Recursive formula of a geometric sequence is given by,
[tex]a_n=a_{n-1}(r)[/tex]
Here, [tex]a_n=[/tex] nth term of the sequence
[tex]a_{n-1}=[/tex] (n - 1)th term
r = common ratio
Therefore, recursive formula for the given sequence will be,
[tex]a_1=2[/tex]
[tex]a_n=a_{n-1}(2.5)[/tex]
Explicit formula of a geometric sequence is given by,
[tex]a_n=a_1(r)^{n-1}[/tex]
Therefore, explicit formula of the sequence will be,
[tex]a_n=2(2.5)^{n-1}[/tex]
Option (2) will be the correct option.