#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# 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.

Arun Kumar IIT Delhi
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