Let the 2nd, 8th and 44th terms of a non-constant A.P. be respectively the 1st, 2nd and 3rd terms of a G.P. If the first term of the A.P. is 1, then the sum of its first 20 terms is equal to:
Solutions · 1
Official solution
Let common difference d. (1+7d)2=(1+d)(1+43d):
\[1+14d+49d^2 = 1+44d+43d^2 \implies 6d^2-30d=0 \implies 6d(d-5)=0.\]
Since the A.P. is non-constant, d=5.
\[S_{20} = \frac{20}{2}\big[2(1)+19(5)\big] = 10(97) = 970.\]