Given:
Sum of G.P = 3069/512
Where, a = 3, r = (3/2)/3 = 1/2, n = ?
By using the formula,
Sum of GP for n terms = a(rn – 1 )/(r – 1)
3069/512 = 3 ((1/2)n – 1)/ (1/2 – 1)
3069/512 × 3 × 2 = 1 – (1/2)n
3069/3072 – 1 = – (1/2)n
(3069 – 3072)/3072 = – (1/2)n
-3/3072 = – (1/2)n
1/1024 = (1/2)n
(1/2)10 = (1/2)n
10 = n
∴ 10 terms are required to make 3069/512
