Question

The product of three consecutive terms of a $\text{G.P.}$ is $512.$ If $4$ is added to each of the first and the second of these terms, then the three terms now form an $\text{A.P.}$ Then the sum of the original three terms of the given $\text{G.P.}$ is:

• A. $36$
• B. $32$
• C. $28$
• D. $24$

Answer 1

The correct option is C $28$

Let three terms of $\text{G.P.}$ are
$\frac{a}{r},a,ar$
$\therefore a^3=512$
$\Rightarrow a=8$
Now, term of $\text{G.P.}$ are
$\frac{8}{r},8,8r$
As per question,
$\frac{8}{r}+4,12,8r$ are in $\text{A.P.}$
$\therefore 24=8r+(\frac{8}{r}+4)$
$\Rightarrow 2r^2-5r+2=0$
$\Rightarrow r=2,\frac{1}{2}$
$\therefore 16,8,4$ are the $3$ terms of given $\text{G.P.}$
Hence, sum of terms = $28$