Question

Find the four no,s in a.p whose sum is 50 and in which the greatest no. is 4 times the least

Answer 1

let the 4 no's be a-3d , a-d , a+d , a+3d
then a-3d+a-d+a+d+a+3d=50 
4a=50
a=25/2
but a+3d=4(a-3d)
a+3d=4a-12d
3a=15d
a=5d
25/2=5d
d=5/2 
so the 4 no's are
a-3d=25/2-15/2=10/2=5
a-d=25/2-5/2=20/2=10
a+d= 25/2+5/2=15
a+3d= 25/2+15/2=20

Answer 2

let the 4 number be a - 3d , a - d , a + d , a +3 d
then a - 3d +a - d + a + d +  a + 3d=50 
4a=50
a=25/2
but a + 3d = 4(a-3d)
a + 3d = 4a - 12d
3a=15d
a=5d
25/2=5d
d=5/2 
so the 4 no's are
a-3d=25/2-15/2=10/2=5
a-d=25/2-5/2=20/2=10
a+d= 25/2+5/2=15
a+3d= 25/2+15/2=20