Discussion
The first term of a G.P. is 1. The sum of the third and fifth term is 90. Find the common ratio.
Answer: B
Given \(a=1\). The third term is \(ar^2 = r^2\) and the fifth term is \(ar^4 = r^4\). Given \(r^2 + r^4 = 90\). Let \(x=r^2\). The equation is \(x+x^2=90 \Rightarrow x^2+x-90=0 \Rightarrow (x+10)(x-9)=0\). Since \(x=r^2\), it cannot be negative. So \(x=9\). \(r^2=9\), which gives \(r = \pm 3\).
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