Mathematics - Sequence & Series Question with Solution | TestHub

Let term be$a-2d,a-d,a,a+d,a+2d$
Sum$=25\Rightarrow 5a=25\Rightarrow a=5$
Product$=2520$
$\left(5-2d\right)\left(5-d\right)5\left(5+d\right)\left(5+2d\right)=2520$
$\Rightarrow \left(25-4d^2\right)\left(25-d^2\right)=504$
$\Rightarrow 625-100d^2-25d^2+4d^4=504$
$\Rightarrow 4d^4-125d^2+625-504=0$
$\Rightarrow 4d^4-125d^2+121=0$
$\Rightarrow 4d^4-121d^2-4d^2+121=0$
$\Rightarrow \left(d^2-1\right)\left(4d^2-121\right)=0$
$\Rightarrow d=\pm 1,d=\mp \frac{11}{2}$
$d=\pm 1,$does not give$-\frac{1}{2}$as a term
$\therefore d=\frac{11}{2}$
$\therefore$Largest term$=5+2d=5+11=16$