Question

Find an explicit formula for the geometric sequence -8,-40,-200,-1000

Answer 1

An explicit formula for the given geometric sequence, $a_{n} =\dfrac{-8}{5} (5)^{n}$

Step-by-step explanation:

The given geometric sequence:

- 8, - 40, - 200, - 1000

Here, first term(a) = - 8, common ration(r) = $\dfrac{-40}{-8}$ = 5

To find, an explicit formula for the given geometric sequence = ?

We know that,

The explicit formula for the geometric sequence

$a_{n} =ar^{n-1}$

∴ An explicit formula for the given geometric sequence

$a_{n} =(-8)(5)^{n-1}$

$a_{n} =\dfrac{-8}{5} (5)^{n}$

∴ An explicit formula for the given geometric sequence, $a_{n} =\dfrac{-8}{5} (5)^{n}$