Question

Sum to infinity of a G.P is $15$, whose first term is $a$ then a MUST satisfy the inequality given by

• A. $0<a<130$
• B. $0<a<30$
• C. $0<a<15$
• D. $0<a<100$

Answer 1

The correct option is C $0<a<15$

given $a+ar+a{r}^2+a{r}^3+.......=15$

where $0<r<1\frac{a}{1-r}=15$

$(\because |r|⩾1$, geometric series is divergent $)$

$a=15(1-r)$

when $0<r<1$

$\Rightarrow -1<-r<0.$

$\Rightarrow 0<1-r<1$

$\therefore 0<15(1-r)<15$

$\Rightarrow 0<a<15$