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.

Asked by Sakshi | 1 year ago |  52

##### Solution :-

Given:

Sum of GP = 728

Where, r = 3, a = ?

Firstly,

Tn = arn-1

486 = a3n-1

486 = $$\dfrac{ a3^n}{3}$$

486 (3) = a3n

1458 = a3n …. Equation (i)

By using the formula,

Sum of GP for n terms = $$\dfrac{ a(r^n – 1 )}{(r – 1)}$$

728 = $$\dfrac{ a (3^n – 1)}{2}$$

1456 = a3n – a … equation (2)

Subtracting equation (1) from (2) we get

1458 – 1456 = a.3n – a.3n + a

a = 2.

The first term is 2

Answered by Sakshi | 1 year ago

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