Let a, a r, a r^2 , be an infinite G.P. If _ n=0 ^ a r^n=57 and _ n=0 ^ a^3 r^ 3 n =9747 , then a+18 r is equal to

Step-by-step solution

aligned & _ n=0 ^ ar ^ n =57 & a + ar + ar ^2+ =57 & a 1- r =57 (I) & _ n =0 ^ a ^3 r ^ 3 n =9747 & a ^3+ a ^3 r ^3+ a ^3 r ^6+ . =9746 & a ^3 1- r ^3 =9746 (II) & ( I )^3 ( II ) a ^3 (1- r )^3 a ^3 1- r ^3 = 57^3 9717 =19 & a =19 & a +18 r =19+18 2 3 =31 & aligned On solving, r = 2 3 and r = 3 2 (rejected ) aligned & a=19 & a+18 r=19+18 2 3 =31 aligned