# The common ratio

‘Tn’ represents the nth term of a G.P. series.

Tn = arn-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. ‘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.  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

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