Answer : Tn represents the nth term of a G.P. series.

r = 6 ÷ 3 = 2

Tn = ar^n-1

⇒1536 = 3 × 2n-1

⇒1536 ÷ 3 = 2n ÷ 2

⇒1536 ÷ 3 × 2 = 2n

⇒1024 = 2n

⇒210 = 2n

∴ n = 10

Sum of a G.P. series is represented by the formula, when r>1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.

Here, a = 3

r = 2

n = 10 terms