Question

The first term of a G.P is 1.The sum of the Third term and the fifth term is 90,Find the common Ratio of the G.P

Answer 1

Let first term be a = 1; and common ratio = d;

Then, 

      ad² + a = 90

=> + d² - 90 = 0

=> + 10d² - 9d² - 90 = 0

=> (d² - 9) (d² + 10) = 0

=> d² = 9     {Neglecting -10}

=> d = ±3 Hence, the common ratio is ±3.

____

Answer 2

Answer:

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

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.