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Mathematics

If the 5th term of a G.P. is 2, then the product of its first nine terms is :

  1. 256

  2. 1024

  3. 512

  4. 2048

G.P.

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Answer

Let first term and common ratio of G.P. be a and r respectively.

Given,

5th term of a G.P. is 2.

⇒ T5 = 2

⇒ ar5 - 1 = 2

⇒ ar4 = 2 …..(1)

Product of first 9 terms = a × ar1 × ar2 × …… × ar8

⇒ a9.r0 + 1 + 2 + …. + 8

⇒ a9.r36

⇒ (ar4)9 …..(2)

Substituting value of ar4 from equation (1) in (2), we get :

⇒ (2)9

⇒ 512.

Hence, option 3 is the correct option.

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