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