Question

HELP! Find the 11th term in the geometric sequence in which a3 is 24 and a5 is 96

Answer 1

a₁₁ = 6144

Explanation:

The n th term of a geometric sequence is

`a_(n)` = a₁
`r^(n-1)`

where a₁ is the first term and r the common ratio

Given a₃ = 24 and a₅ = 96 , then

a₁r² = 24 → (1)

a₁
`r^(4)` = 96 → (2)

Divide (2) by (1)

`(ar^4)/(ar^2)` =
`(96)/(24)` , that is

r² = 4 , thus

r = 2

substitute r = 2 into (1)

4a₁ = 24 ( divide both sides by 4 )

a₁ = 6

Thus

a₁₁ = 6 ×
`2^(10)` = 6 × 1024 = 6144