Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series

If 5 2^8 3¹⁶ is one of the terms of a G.P. whose first term is 5 and all its terms are natural number then possible common ratio of the G.P. is:

Options

A6
B12
C18
D(324)^2

Correct answer

D. (324)^2

Step-by-step solution

aligned & a=5 & T_ r+1 =5 r^ n-1 =5 2^8 3¹⁶ & r^ n-1 = (2 3^2 )^8= ( (2 3^2 )^2 )^4= ( (2 3^2 )^4 )^2= ( (2 3^2 )^8 )^1 aligned Possible common ratio of the G.P. are 2 3^2, (2 3^2 )^2, (2 3^2 )^4, (2 3^2 )^8

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