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The 4th and 8th term of a G.P. are 24 and 8/27 respectively. find the 1st term and common ratio

User Tom Ekberg
by
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1 Answer

5 votes

Answer:

see explanation

Explanation:

The n th term of a geometric progression is


a_(n) = a₁
r^(n-1)

where a₁ is the first term and r the common ratio

given a₄ = 24, then

a₁
r^(3) = 24 → (1)

Given a₈ =
(8)/(27), then

a₁
r^(7) =
(8)/(27) → (2)

Divide (2) by (1)


r^(4) =
((8)/(27) )/(24) =
(1)/(81)

Hence r =
\sqrt[4]{(1)/(81) } =
(1)/(3)

Substitute this value into (1)

a₁ × (
(1)/(3) )³ = 24

a₁ ×
(1)/(27) = 24, hence

a₁ = 24 × 27 = 648

User Charnould
by
8.4k points

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