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

⇒ *a*^{3} + *a*^{3}*r*^{3} + *a*^{3}*r*^{6}+ ......... = 192

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

⇒ 2*r*^{2} + 5*r* + 2 = 0

⇒ (2*r* + 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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