Q. 94.3( 3 Votes )

# 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 :

Given: Common Ratio = 3

Sum of GP = 728

Sum of GP for n terms =

Last term say it be n

∴ T_{n} = ar^{n - 1}

⇒ 486 = a3^{n - 1}

⇒

⇒ 1458 = a.3^{n} …(1)

⇒

⇒

⇒ 1456 = a.3^{n} - a…(2)

Subtracting 1 from 2 we get

⇒ 1458 - 1456 = a.3^{n} - a.3^{n} + a

⇒ a = 2.

∴ The first term is 2.

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