# 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, $$0<x<10$$