Question

Find the 8th term of the geometric sequence shown below. -2x^5, 4x^10, -8x^15

Answer 1

a₈ = 256
`x^(40)`

Explanation:

the nth term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

here a₁ = - 2
`x^(5)` and r =
`(a_(2) )/(a_(1) )` =
`(4x^(10) )/(-2x^(5) )` = - 2
`x^(5)` , then

a₈ = - 2
`x^(5)`
`(-2x^5)^(7)`

= - 2
`x^(5)` [
`(-2)^(7)` ×
`x^(5(7))` ]

= - 2
`x^(5)` × - 128
`x^(35)`

= 256
`x^(40)`