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In an infinite GP series, each term is equal to three times the sum of all the terms that follow it and the sum of the first two terms is 15. find the sum of the series to infinity.

In an infinite GP series, each term is equal to three times the sum of all the terms that follow it and the sum of the first two terms is 15. find the sum of the series to infinity.

Grade:10

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello Student,

\\g_1,g_2,g_3,g_4,g_5,g_6.......g_\infty \\g_1+g_2=15 \\g_1=3(\sum_{1}^{\infty}g-g_1)=3(sum_\infty-g_1) \\=3({g_1 \over 1-r}-g_1)=3({rg_1 \over 1-r}) \\=>3({r \over 1-r})=1 \\=>3r=1-r \\=>r={1 \over 4} \\g_1+g_2=15 \\=>g_1(1+r)=15 \\=>g_1{ 5 \over 4}=15 \\=>g_1=12 \\=>\sum g={a \over 1-r}={12 \over {3\over 4}}=16
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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