Find the geometric series whose 5th and 8th terms are 80 and 640 respe

1.	Find the geometric series whose 5th and 8th terms are 80 and 640 respectively.
Answer» The nth term of a GP is an = ar^n-1 It’s given in the question that 5th term of the GP is 80 and 8th term of GP is 640. So, a₅ = ar⁴ = 80 → (1) a₈ = ar⁷ = 640 → (2) \(\cfrac{(2)}{(1)}_\longrightarrow \cfrac{ar^7}{ar^4}\) = r³ = \(\cfrac{640}{80}\)= 8 Common ratio, r = 2, ar⁴ = 80 16a = 80 a = 5 The required GP is of the form a, ar, ar² , ar³ , ar⁴…. First term of GP, a = 5 Second term of GP, ar = 5 x 2 =10 Third term of GP, ar² = 5 x 2² = 20 Fourth term of GP, ar³ = 5 x 2³ = 40 Fifth term of GP, ar⁴ = 5 x 2⁴= 80 And so on... The required GP is 5, 10, 20, 40, 80…

Find the geometric series whose 5th and 8th terms are 80 and 640 respectively.

Answer»

The nth term of a GP is an = ar^n-1

It’s given in the question that 5th term of the GP is 80 and 8th term of GP is 640.

So, a₅ = ar⁴ = 80 → (1)

a₈ = ar⁷ = 640 → (2)

\(\cfrac{(2)}{(1)}_\longrightarrow \cfrac{ar^7}{ar^4}\) = r³ = \(\cfrac{640}{80}\)= 8

Common ratio, r = 2,

ar⁴ = 80

16a = 80 a = 5

The required GP is of the form a, ar, ar² , ar³ , ar⁴….

First term of GP, a = 5

Second term of GP, ar = 5 x 2 =10

Third term of GP, ar² = 5 x 2² = 20

Fourth term of GP, ar³ = 5 x 2³ = 40

Fifth term of GP, ar⁴ = 5 x 2⁴= 80

And so on...

The required GP is 5, 10, 20, 40, 80…