Question

Five numbers are in A.P., whose sum is $25$ and product is $2520$. If one of these five numbers is $-\frac{1}{2}$, then the greatest number amongst them is

• A. $16$
• B. $27$
• C. $7$
• D. $\frac{21}{2}$

Answer 1

The correct option is A $16$

Let five numbers be $a-2d,a-d,a,a+d,a+2d$
$5a=25$
$\Rightarrow a=5$

$(a-2d)(a-d)a(a+d)(a+2d)=2520$
$\Rightarrow (25-4d^2)(25-d^2)=504$
$\Rightarrow 4d^4-125d^2+121=0$
$\Rightarrow 4d^4-4d^2-121d^2+121=0$
$\Rightarrow d^2=1$ or $d^2=\frac{121}{4}$
$\Rightarrow d=\pm 1,\pm \frac{11}{2}$
For $d=\frac{11}{2},a+2d$ is the greatest term.
$a+2d=5+11=16$