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  • The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

9.  The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

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Given: The first term of a G.P. is 1. The sum of the third term and fifth term is 90.

a=1

a_3=a.r^2=r^2                                      a_5=a.r^4=r^4

\therefore \, \, r^2+r^4=90

\therefore \, \, r^4+r^2-90=0

\Rightarrow \, \, r^2=\frac{-1\pm \sqrt{1+360}}{2}

       r^2=\frac{-1\pm \sqrt{361}}{2}

      r^2=-10 \, or \, 9

r=\pm 3

Thus, the common ratio of GP is \pm 3.

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seema garhwal

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