In a geometric sequence a2=-320 and a5=625. write the explicit formula for the sequence

The sequence is given by,

f(n) =

Step-by-step explanation:

Let the geometric sequence has 1st term = b and common ratio = r

so, the sequence is,

f(n) = ----------------------(1)

According to the question,

---------------------(2)  and,

= 625

⇒ = 625 --------------(3)

Now, dividing (3) by (2), we get,

⇒

⇒

⇒ r = 1.25 -----------------------------------(4)

Now, from (2) and (4), we get,

b =

⇒ b =

⇒ b = 256-----------------(5)

So, from (4) and (5), the sequence is given by,

f(n) =