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NCERT Class XI Mathematics - Sequences and Series - Solutions

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Question : 33 of 106
Marks: +1, -0
Find the 20th and nth terms of the G.P. 52,54,58\frac{5}{2},\frac{5}{4},\frac{5}{8} , ...
Solution:  
The given G.P. is 52,54,58\frac{5}{2},\frac{5}{4},\frac{5}{8} , ... . Let a be the first term and r be the common ratio of G.P.
Here a = 52\frac{5}{2} and r = 5452\frac{\frac{5}{4}}{\frac{5}{2}} = 12\frac{1}{2}
Then nth term is
ana_n = arn−1ar^{n-1} = 52(12)n−1\frac{5}{2}\left(\frac{1}{2}\right)^{n-1} = 5 (12)n\left(\frac{1}{2}\right)^n = 52n\frac{5}{2^n}
and 20th term is a20a_{20} = 5220\frac{5}{2^{20}}
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