If four numbers in A.P. are such that their sum is 50 and the greatest

1.	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 :A. 5, 10, 15, 20 B. 4, 10, 16, 22 C. 3, 7, 11, 15 D. none of these
Answer» Option : (A) 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

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 :A. 5, 10, 15, 20 B. 4, 10, 16, 22 C. 3, 7, 11, 15 D. none of these

Answer»

Option : (A)

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