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» Correct answer is A. 5,10,15,20 Let the 4 numbers be a, a + d, a + 2d, a + 3d. Sum of 4 numbers in A.P = 50 a + a + d + a + 2d + a + 3d = 50 ⇒ 4a + 6d = 50 ⇒ 2a + 3d = 25 --------------(1) Given the greatest number is 4 times the least. 4(a) = a + 3d 4a – a = 3d a = d Putting, a = d in (1), we obtain 5d = 25 d = 5 ⇒ a = 5 ∴ First four terms are 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»

Correct answer is A. 5,10,15,20

Let the 4 numbers be a, a + d, a + 2d, a + 3d.

Sum of 4 numbers in A.P = 50

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

⇒ 4a + 6d = 50

⇒ 2a + 3d = 25 --------------(1)

Given the greatest number is 4 times the least.

4(a) = a + 3d

4a – a = 3d

a = d

Putting, a = d in (1), we obtain

5d = 25

d = 5

⇒ a = 5

∴ First four terms are 5, 10, 15, 20.