An infinite G.P. has first term ‘x’ and sum ‘5’, then x belongs to
1). 0 ≤ x ≤ 10
2). -10 < x < 0
3). 0 < x < 10
4). -10 ≤ x ≤ 0
$(\frac{{\rm{x}}}{{1 - {\rm{r}}}} = 5 \Rightarrow {\rm{r}} = 1 - \frac{{\rm{x}}}{5})$
Since G.P. contains infinite terms
∴ –1 < r < 1
$(\Rightarrow - 1 < 1 - \frac{{\rm{x}}}{5} < 1 \Rightarrow - 2 < - \frac{{\rm{x}}}{5} < 0)$
⇒ -10 < - x < 0
⇒ 0 < x < 10