In an A.P, cum of four consecutive terms is 28 and their sum of their square is 276. find the four number

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In an A.P, sum of four consecutive term is 28 and their sum of their squares is 276. find the four number.


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Salim Ahmed Kawsar

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Let the numbers be: a - 3d, a - d, a + d, a + 3d

a - 3d + a - d + a + d + a + 3d = 32

4a = 32

\(\therefore\) a = 8

(a - 3d)2 + (a - d)2 + (a + d)2 + (a + 3d)2 = 276

4a2 + 20d2 = 276

20d2 = 276 - 4(8)2 = 20

\(\therefore\) d = 1

Therefore the 4 numbers are:

a - 3d, a - d, a + d, a + 3d = 8 - 3, 8 - 1, 8 + 1, 8 + 3 = {5, 7, 9, 11 }

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