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