Question

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

Answer 1

an = (-8/5) × 5^n

Explanation:

It is Geometric progression with:

first term: -8

common ratio: -40/-8 = 5

an = (-8) × 5^(n-1)

an = (-8/5) × 5^n

Answer 2

`a_(n)` = - 8
`(5)^(n-1)`

Explanation:

The n th term ( explicit formula ) of a geometric sequence is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

Here a = - 8 and r = - 40 ÷ - 8 = 5, thus

`a_(n)` = - 8
`(5)^(n-1)`