Question

If the first term of a GP is 5 and the sum of the first three terms is 31/ 5, find the common ratio.

Answer 1

1/5 or -6/5

let the common ratio be r

5 , 5r ,5r^2

5 + 5r +5r^2 =31/5

5(r +r^2) = 31/5 - 5 =31/5 - 25/5 =6/5

r (r+1) = 6/25 = 1/25 + 5/25 = 1/5 (1/5 + 1)

on comparing r=1/5

also 6/25 = 36/25 -30/5 = -6/5 (-6/5 +1)

so r= -6/5 also

r= 1/5 or -6/5

you can silve it using quadratic equations also .. Here i am used the most simple one

Like if satisifed