Question

Find the fifth term and the nth term of the geometric sequence whose initial term a, and common ratio r are given.

a₁ = 5, r=2

Answer 1

a₅ = 80 ,
`a_(n)` = 5
`(2)^(n-1)`

Explanation:

to find a term in the geometric sequence multiply the previous term by r

a₁ = 5

a₂ = a₁ × 2 = 5 × 2 = 10

a₃ = a₂ × 2 = 10 × 2 = 20

a₄ = a₃ × 2 = 20 × 2 = 40

a₅ = a₄ × 2 = 40 × 2 = 80

the nth term of a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

here a₁ = 5 and r = 2 , then

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