Question

The sum of the first 3 terms of a G.P. is 27 and the sum of the fourth, fifth and sixth terms is -1. Find the common ratio and the sum to infinity of the G.P.

Answer 1

Answer:

Step-by-step explanation:

Let r be the common ratio of the G.P. It is given that the first term a=1.

Now, a  

3

​

+a  

5

​

=90

⇒ar  

2

+ar  

4

=90

⇒r  

2

+r  

4

=90

⇒r  

4

+r  

2

−90=0

⇒r  

4

+10r  

2

−9r  

2

−90=0

⇒(r  

2

+10)(r  

2

−9)=0

⇒r  

2

−9=0

⇒r=±3

Hence, the common ratio of the given G.P. is 3 or −3.