NCERT Class XI Mathematics - Sequences and Series - Solutions

Question : 58

Total: 106

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1) th to (2n) th term is

Solution:

Let the G.P. be a, ar, ar2, .......
Sum of first n terms = a + ar +...... + arn−1 ⇒ Sn =

a(1−rn)

1−r

Let the sum of terms from (n + 1)th term to (2n)th term denoted by
Sn′ = arn+arn+1 + ... + ar2n−1
∴ Sn′ =

arn(1−rn)

1−r

. Now ,

Sn′

a(1−rn)

1−r

arn

(1−rn)

1−r

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