The sum of the terms of an infinite G.P is 7 and the sum of the cubes of the terms is 1,225. Find the first term of the series. Choose the most appropriate option:
A) 35/3 B) 35/2 C) 15/2 D) 9/4 E) 7/4
S a = a/ ( 1 – r ) = 7 …………. (1)   Sum to infinity of the cubes = a 3 / 1 –r 3 = 1,225   From (1) a 3 / ( 1 – r ) 3 = 7 3 = 343   Therefore, ( 1 – r ) 3 / 1 – r 3 = 1225/343,   (1+ r 2 -2r)/ ( 1 + r 2 + r ) = 25/7   7 + 7 r 2 –14r = 25 + 25 r + 25 r 2   18 r 2 +39r + 18 = 0, on solving r = -3/2 or -2/3   for an infinite G.P | r | &lt; 1, r = - 2/3   Therefore, a / [ 1 – ( - 2/3 ) ] = 7, a = 7 * 5/3 = 35/3 35/3NSWER:35/3
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The sum of the terms of an infinite G.P is 7 and the sum of the cubes of the terms is 1,225. Find the first term of the series.