# Find the four numbers in A.P. whose sum is 50 and in which the greatest number is 4 times the least.

Let the four numbers be (a – 3d), (a – d), (a + d) and (a + 3d)

a – 3d + a – d + a + d + a + 3d = 50

4a = 50

a =

According to question,

(a + 3d) = 4(a – 3d)

a + 3d = 4a – 12d

3a = 15d

5d =

d =

Therefore,

a – 3d = - = 5

a – d = - = 10

a + d = + = 15

a + 3d = + = 20

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