Q. 113.8( 17 Votes )

# Find four numbers in AP whose sum is 28 and the sum of whose squares is 216.

Answer :

Let the numbers be (a - 3d), (a - d), (a + d), (a + 3d).

Now, sum of the numbers = 28

(a - 3d) + (a - d) + (a + d) + (a + 3d) = 28

4a = 28

a = 7

Now, sum of the squares of the terms = 216

(a - 3d)2 + (a - d)2 + (a + d)2 + (a + 3d)2= 216

a2 + 9d2 - 6ad + a2 + d2 - 2ad + a2 + d2 + 2ad + a2 + 9d2 + 6ad = 216

4a2 + 20d2 = 216

Put the value of a = 7, we get,

4(49) + 20d2 = 216

20d2 = 216 - 196

20d2 = 20

d2 = 1

d = 1

If d = 1, then the numbers are 4, 6, 8, 10.

If d = - 1, then the numbers are 10, 8, 6, 4.

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