Question

Write a rule for the nth term of the geometric sequence for which a1=11 and a4=88

Answer 1

`a_(n)` = 11
`(2)^(n-1)`

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

given a₁ = 11 and a₄ = 88 , then

11 r³ = 88 ( divide both sides by 8 )

r³ = 8 ( take cube root of both sides )

r =
`\sqrt[3]{8}` = 2 , then the nth term is

`a_(n)` = 11
`(2)^(n-1)`