Question

Write an equation for the nth term of each geometric sequence:

1) 2,-6,18,…
2) 5,10,20,…

Answer 1

see explanation

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

(1)

a₁ = 2 and r =
`(a_(2) )/(a_(1) )` =
`(-6)/(2)` = - 3 , then

`a_(n)` = 2
`-3)^(n-1)`

(2)

a₁ = 5 and r =
`(10)/(5)` = 2 , then

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