Question

The common ratio of a G.P. is 3, and the last term is 486. If the sum of these terms be 728, find the first term.

Answer 1

Given:

Sum of GP = 728

Where, r = 3, a = ?

Firstly,

T_n = ar^n-1

486 = a3^n-1

486 = a3ⁿ/3

486 (3) = a3ⁿ

1458 = a3ⁿ …. Equation (i)

By using the formula,

Sum of GP for n terms = a(rⁿ – 1 )/(r – 1)

728 = a (3ⁿ – 1)/2

1456 = a3ⁿ – a … equation (2)

Subtracting equation (1) from (2) we get

1458 – 1456 = a.3ⁿ – a.3ⁿ + a

a = 2.

∴ The first term is 2