An infinite G.P has first term 'x' and sum '5' , then x belongs to : a) 010 c) ∣x∣<10 d) −10

Option a) 0<x<10
The sum of infinite terms of GP is given by
\(S_{\infty}=\frac{a}{1-r};r< 1\)\(S_{\infty}=\infty;\left |r \right |\geq 1\)\(S_{\infty}=\frac{x}{1-r}=5\)\(since \left | r \right |< 1\)1−r=x/5
\(-1< \frac{5-x}{5}< 1\)\(-5<{5-x}<5\)\(-10<-x<0\)Therefore, \(0<x<10\)

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