The sum of an infinite number of terms of GP is 4 and the sum of their cubes is 192. Find the series.

Let a be the first term and r be the common ratio of the given G.P. then,

Sum = 4

 

Sum of cubes = 192

a3 + a3r3 + a3r6+ ......... = 192

 

Dividing the cube of (1) by (2) we get

⇒ 2r2 + 5r + 2 = 0

⇒ (2r + 1) (r + 2) = 0

Since r ≠ – 2 because –1 < r < 1 for an infinite G.P.

 

Hence the G.P. is

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