Question

The sum to infinity of the terms of an infinite geometric progression is $6$. The sum of the first two terms is $4\frac{1}{2}$. The first term of the progression is

• A. $3$ or $1\frac{1}{2}$
• B. $1$
• C. $2\frac{1}{2}$
• D. $6$
• E. $9$ or $3$

Answer 1

Answer: (E)

$9$ or $3$

Let the first two terms be $a$ and $ar$ where $-1<r<1$.
$\therefore a(1+r)=4\frac{1}{2}$
Since $s=a/(1-r)=6,a=6(1-r)$
$\therefore 6(1-r)(1+r)=4\frac{1}{2};\therefore r=\pm \frac{1}{2};\therefore a=3$ or $9$.