Question

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

Answer 1

256(-5/4)^n-1

Answer 2

The sequence is given by,

f(n) =
`256 * (1.25)^((n - 1))`

Explanation:

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

so, the sequence is,

f(n) =
`b * r^((n - 1))` ----------------------(1)

According to the question,

`br = 320` ---------------------(2) and,

`b * r^((5 - 1))` = 625

⇒
`b * r^(4)` = 625 --------------(3)

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

`r^(3) = \frac {625}{320}`

⇒
`r^(3) = \frac {125}{64}`

⇒
`r = \frac {5}{4}`

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

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

b =
`\frac {320}{1.25}`

⇒ b =
`320 * \frac {4}{5}`

⇒ b = 256-----------------(5)

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

f(n) =
`256 * (1.25)^((n - 1))`