Question

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 1

Answer:

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Answer 2

A. 5, 10, 15, 20

Step-by-step explanation:

Given: If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least

Solution:

n = 4

S4 = 50

4a = L

S4 = 4/2 (a + L)

50  = 2 (a + 4a)

50 = 2(5a)

Therefore a = 50/10 = 5.

L = 4a = 20.

L = a + 3d = 5 + 3d = 20

 3d = 15

Therefore d = 5.

So the AP will be 5, 10, 15, 20

Option A is the answer.