Question

The terms in geometric progression are such that their sum is $26$ and their product is $216$. Find the terms.

• A. $4,8,16$
• B. $2,6,18$
• C. $2,8,16$
• D. $3,6,12$

Answer 1

The correct option is B $2,6,18$

$a,ar,a{r}^2$

$=>a+ar+a{r}^2=26$

$=>(ar{)}^3=216$

$=>ar=6$

$=>a+ar+a{r}^2=26$

$=>a+a{r}^2=20$

$=>a(1+r^2)=20$

$=>\frac{6}{r}(1+r^2)=20$

$=>\frac{6}{r}+6r-20=0$

$=>6r^2-20r+6=0$

$=>3r^2-10r+3=0$

$=>3r^2-9r-r+3=0$

$=>3r(r-3)-1(r-3)=0$

$r=3,r=\frac{1}{3}$

$a=2$

Terms are $2,6,18$