Question

The sum of six terms of a geometric sequence is -63. If the first term is 3, find the common ratio.

Please explain to me the steps on how I could solve for the common ratio; thank you!

Answer 1

a geometric progression is one where the terms are :
\[a ,ar, ar ^{2},ar ^{3}...ar ^{n}\]

where a is the first term and r is the common ratio
in a GP
sum of n terms is given by \[(a(1-r ^{n}))/(1-r)\]

putting this equal to -63 and a as 3, you can find the value of r

Answer 2

take n as 6

Answer 3

oh okay! thanks :)