NCERT Class XI Mathematics - Sequences and Series - Solutions

Question : 87

Total: 106

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

Solution:

Let a be the first term and r be the common ratio of the G.P.
According to question, a = 1, a3+a5 = 90
⇒ ar2+ar4 = 90 ⇒ 1r2+1r4 = 90 ⇒ r4+r2 – 90 = 0 ⇒ (r2 – 9) (r2 + 10) = 0
⇒ r2 = 9, – 10 but r2 ≠ –10
∴ r2 = 9 ⇒ r = ± 3.
Hence the common ratio of G.P. is ± 3.

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