Question

find th four numbers in ap whose sum is 50 and in which the greatest number is 4 times the least

Answer 1

We know that ,

a+(n-1)d

1st term= a

2nd term=a+d

3rd term= a+2d

4th term= a+3d

Sum of four numbers= 50

a+a+d+a+2d+a+3d=50

4a+6d=50

2a+3d=25-----(1)

It is also given that the greatest no. is 4 times the least so,

1st term × 4= 4th term

a×4 = a+3d

4a=a+3d

4a-a=3d

3a=3d

a=d

Putting a=d in eq. 1

2a+3d=25

2d+3d=25

5d=25

d=5  

and a=d

So the 4 terms are:

5, 5+5, 5+2(5), 5+3(5)

5,10,15 and 20.