Question

Divide $28$ into four parts in A.P. so that ratio of the product of first and third with the product of second and fourth is $8:15$.

Answer 1

Here $4a=28$
$\therefore a=7$
Also $\frac{(a-3d)(a+d)}{(a-d)(a+3d)}=\frac{8}{15}$
or $15[a^{2}3d^2-2ad]=8[a^2-3d^2+2ad]$
or $7(a^2-3d^2)=46ad$
or $7(49-3d^2)=46\times 7$d
or $49-3d^2=46d$ or $3d^2+46d-49=0$
$(d-1)(3d+49)=0$
$\therefore d=1$
$\therefore$ Required numbers are $4,6,8,10$.