Question

Find the four numbers in A.P. whose sum is 50 and in which the greatest number is 4 times the least.

Answer 1

Let the four numbers in A.P. be
Sum = 50
$\Rightarrow a-3d,a-d,a+d,a+3d\Rightarrow (a-3d)+(a+d)+(a+d)+(a+3d)=50\Rightarrow 4a=50$
$a=\frac{25}{2}\dots \dots \left(i\right)$
and
$(a+3d)=4(a-3d)\frac{25+6d}{2}=50-12d30d=75d=\frac{25}{10}=\frac{5}{2}\dots \dots \left(ii\right)$
The terms are as follows
$(\frac{25}{2}-\frac{3\times 5}{2}),(\frac{25}{2}-\frac{5}{2}),(\frac{25}{2}+\frac{5}{2}),(\frac{25}{2}+\frac{3\times 5}{2})$
$=5,10,15,20$