Mathematics
If the 5th term of a G.P. is 2, then the product of its first nine terms is :
256
1024
512
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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