‘T_n’ represents the n^th term of a G.P. series.

T_n = ar^n-1

⇒486 = a(3)^n-1

⇒486 = a( 3ⁿ ÷ 3) )

⇒486 × 3 = a(3ⁿ)

⇒1458 = a(3ⁿ ) ………(i)

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

∴

⇒

⇒728 × 2 = a (3ⁿ)-a …… [ Putting a(3ⁿ ) = 1458 fromk (i) ]

⇒1456 = 1458 -a

⇒1456-1458 = -a

⇒-2=-a [ Multipying both sides by -1]

⇒a = 2