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

$\text{Let the four numbers in A.P be a, a+d, a+2d, a+3d}$

$\text{As per given data,}$

$\text{a+(a+d)+(a+2d)+(a+3d)=50}$

$\implies\text{4a+6d=50}$

$\implies\textbf{2a+3d=25}$....(1)

$\text{Also, a+3d=4a}$

$\text{3d=3a}$

$\textbf{d=a}$............(2)

$\text{Using (2) in (1), we get}$

$\text{2a+3a=25}$

$\text{5a=25}$

$\implies\textbf{a=5}$

$\textbf{Then, d=5}$

$\therefore\textbf{The required numbers are 5,10,15, 20}$