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

1 Answer

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

Related Questions

Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Class 11 Maths Sequences and Series View Answer

If a is the G.M. of 2 and \( \dfrac{1}{4}\) find a.

Class 11 Maths Sequences and Series View Answer

Find the geometric means of the following pairs of numbers:

(i) 2 and 8

(ii) a3b and ab3

(iii) –8 and –2

Class 11 Maths Sequences and Series View Answer

Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).

Class 11 Maths Sequences and Series View Answer