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

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

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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 = $\frac{25}{2}$

According to question,

(a + 3d) = 4(a – 3d)

a + 3d = 4a – 12d

3a = 15d

5d = $\frac{25}{2}$

d = $\frac{5}{2}$

Therefore,