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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.
3 years ago

Arun Kumar
IIT Delhi
256 Points

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
3 years ago
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