Question

How do i solve this? Question

Two terms of a geometric sequence are a3=12 and a5=48.

What is the value of a17?

Answer 1

a₁₇ = 196608

Explanation:

The nth term of a geometric sequence is = a₁ where a₁ is the first term and r the common ratio.

Given a₃ = 12 and a₅ = 48 , then

a₁ r² = 12 → (1)

a₁ = 48 → (2)

Divide (2) by (1)

= , that is

r² = 4 ( take square root of both sides )

r = 2

substitute r = 2 into (1)

a₁ 2² = 12

4a₁ = 12 ( divide both sides by 4 )

a₁ = 3

Then

a₁₇ = 3 × = 3 × 65336 = 196608

Hence, the correct answer is a₁₇ = 196608

Answer 2

a₁₇ = 196608

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 a₃ = 12 and a₅ = 48 , then

a₁ r² = 12 → (1)

a₁
`r^(4)` = 48 → (2)

Divide (2) by (1)

`(a_(1)r^(4) )/(a_(1)r^(2) )` =
`(48)/(12)` , that is

r² = 4 ( take square root of both sides )

r = 2

substitute r = 2 into (1)

a₁ 2² = 12

4a₁ = 12 ( divide both sides by 4 )

a₁ = 3

Then

a₁₇ = 3 ×
`2^(16)` = 3 × 65336 = 196608