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Grade 10Magical Mathematics[Interesting Approach]

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.

muthhu swami

12 Years agoGrade 10

1 Answer

Arun Kumar

Approved Tutor Answer12 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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