Q. 11

# If the G.P.’s 5, 10, 20, …. And 1280, 640, 320, … have their nth terms equal, find the value of n.

Answer :

GP is given by

a, ar, ar^{2}, ⋯, ar^{n}^{-1}

In the sequence 5, 10, 20, 40, …

First term, a = 5

Common ratio, r

Equate the term to be found with the nnth term.

ar^{n}^{-1}=1280

5 × 2^{n-1} =1280

2^{n-1} = 256

n - 1 = 8

n =9

∴ 9^{th} term is equal.

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(i)

(ii)

(iii)

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