Question

Please Answer ASAP

The first term of a GP is 1, the sum of the third and fifth term is 90. Find the
common ratio.

Answer 1

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

Answer 2

common ratio is -3 or 3

Explanation:

`u_1=1\\\\u_3=u_1*r^2=r^2\\\\u_5=u_1*r^4=r^4\\\\r^2+r^4=90\\\\r^4+r^2-90=0\\\Delta=1+4*90=361=19^2\\\\r^2=(-1-19)/(2) =-10 (exclude\ a\ square\ is\ positive)\\or\\r^2=(-1+19)/(2)=9\\r^2-9=0\\(r-3)(r+3)=0\\So\ r=-3\ or\ r=3\\`