Question

The fifth term of a geometric sequence is 781.25. Each previous term is 1/5 of the value of the current term. Which recursive formula represents the situation?

Answer 1

Let a₁ = the first term.
Because each previous term is 1/5 of the value of the current term, the geometric sequence is
a₁, 5a₁, 25a₁, ..., 
The common ratio is r = 5.
The n-th term is
$a_{n} = a_{1}r^{n-1}$

The fifth term is 781.25. Therefore
a₁*5⁴ = 781.25
625a₁ = 781.25
a₁ = 1.25

Answer:
The recursive formula is
$a_{n+1} = 5a_{n}, \,\, n=1,2, \, ..., \\ where \\ a_{1} = 1.25$

Answer 2

Answer:

$a_n=5a_{n-1}$

Step-by-step explanation:

Given fifth term of a geometric sequence is 781.25.

$a_5= 781.25$.

Also, each previous term is 1/5 of the value of the current term.

Therefore, common ratio would be 5.

But we just need to find the recursive formula .

Recursive formula of a geometric sequence is given by

$a_n=ra_{n-1}$

Plugging value of r in above formula, we get

$a_n=5a_{n-1}$

Therefore, recursive formula would be  $a_n=5a_{n-1}$ represents the situation.