IIT-JEE 2004 ScreeningQuestion 1
An infinite G.P. has first term $x$ and sum $5$, then $x$ belongs to
Sequence and Series · Geometric Progression
Solution
Formulas used. (1) $S_\infty=\frac{x}{1-r}$, valid only for $|r|<1$Step 1 - Ratio. $$\frac{x}{1-r}=5\ \Longrightarrow\ r=1-\frac x5 .$$ Step 2 - Convergence. $$-1<1-\frac x5<1\ \Longrightarrow\ 0<x<10 .$$ Answer: (C)