Question

45) If 5th term of a G.P. is 3*root3, then the product of first nine terms is : (Dec 201
A) 8
B) 27
C) 243 ​

Answer 1

Answer:

27

Step-by-step explanation:

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i) Let the 1st term of the GP be 'a' and its common ratio be 'r'

ii) So its 5th term is: ar⁴ = 3^(1/3) ------------ (1)

iii) Since 5th term is the middle term of first 9 terms, the product of first 9 terms = (5th term)⁹

[Product of all 9 terms = a*ar*ar²*ar³*ar⁴*ar⁵*ar⁶*ar⁷*ar⁸ = a⁹r³⁶ = (ar⁴)⁹]

iv) So substituting from (1), product of 9 terms = {3^(1/3)}⁹ = 3³ = 27