151k views
4 votes
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.​

2 Answers

4 votes

Answer:

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

User Ace Falobi
by
8.1k points
2 votes

Answer:

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

User Dany Khalife
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories