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Mathematics

Which term of the G.P. 2, 8, 32, 128, …….. is 131072?

  1. 9th

  2. 10th

  3. 8th

  4. 12th

G.P.

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Answer

In the given G.P.,

a = 2

r = 82\dfrac{8}{2} = 4

We know that,

Tn = arn - 1

Let nth term be 131072.

⇒ Tn = 131072

⇒ 2.(4)n - 1 = 131072

⇒ (22)n - 1 = 1310722\dfrac{131072}{2}

⇒ 22n - 2 = 65536

⇒ 22n - 2 = 216

Equate exponents:

⇒ 2n - 2 = 16

⇒ 2n = 16 + 2

⇒ 2n = 18

⇒ n = 182\dfrac{18}{2} = 9.

Hence, option 1 is the correct option.

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