Mark the correct alternative in the following:
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
Let 4 numbers of A.P. be the a, a+d, a+2d, a+3d.
Here, given that their sum is 50.
i.e. a+a+d+a+2d+a+3d=50
∴ 4a+6d=50
∴ 2a+3d=25_____(1)
Also, given that the greatest number is 4 times the least.
i.e.4a=a+3d
∴ 3a=3d
∴ a=d
Substituting a=d in (1) we get,
5a=25
∴ a=5
And, d=a=5
So, numbers are a=5;a+d=5+5;a+2d=5+2(5);a+3d=5+3(5)
i.e. 5,10,15,20