NCERT Class XI Mathematics - Sequences and Series - Solutions

Question : 89

Total: 106

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

Solution:

A G.P. consists of an even number of terms and let the terms be a, ar, ar2,ar3 , ... , ar2n−1 i.e., it contains 2n terms.
According to question, Sum of all terms = 5 (sum of odd places terms)
⇒ a + ar+ar2 + ... + ar2n−1 = 5(a+ar2+...+ar2n−2)
⇒

a(1−r2n)

1−r

= 5[

a[1−(r2)n]

1−r2

] ⇒

a(1−r2n)

1−r2

⇒

1−r

(1−r)(1+r)

⇒ r + 1 = 5 ⇒ r = 4

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