Question

The second term of a G.P is 6, and the fifth term is 48, find the common ratio and the 3rd term of the G.P.​

Answer 1

Common ratio = 2, Third term = 12

Explanation:

ar⁴ = 48........ equation 1

ar = 6.......... equation 2

divide equation 1 by equation 2

r³ = 8

r = ³√8

r = 2

To get the third term we must first get the first term

Since ar = 6 and r = 2, then 2a = 6 and a = 3

3rd term = ar²

3 × 2² = 3 × 4 = 12

Answer 2

r = 2 and a₃ = 12

Explanation:

the nth term of a GP is

`a_(n)` = a₁
`r^(n-1)`

where a₁ is the first term and r the common ratio

given a₂ = 6 and a₅ = 48 , then

a₁r = 6 → (1)

a₁
`r^(4)` = 48 → (2)

divide both sides of (2) by (1) to eliminate a₁

`(a_(1)r^(4) )/(a_(1)r )` =
`(48)/(6)` ( cancel r and
`r^(4)` by r )

r³ = 8 ( take cube root of both sides )

r =
`\sqrt[3]{8}` = 2

substitute r = 2 into (1) and solve for a₁

a₁ × 2 = 6 ( divide both sides by 2 )

a₁ = 3

a₂ = a₁ × r = 3 × 2 = 6

a₃ = a₂ × 3 = 12