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Question

The sum of three numbers in A.P. is 15 and the sum of the squares of the extreme terms is 58. Find the numbers.

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Solution

Let ( a - d ) , a , ( a + d ) are three numbers in A.P.
a - d + a + a + d = 15 ( given )

3a = 15

a = 153

a = 5

Sum of the extremes = 58

(ad)2 + (a+d)2 = 58

2( a2 + d2 ) = 58

a2 + d2 = 29

52 + d2 = 29 [ since a = 5 ]

d2 = 29 - 25

d2 = 4

d = ± 2

Therefore, required numbers are:

If a = 5 , d = 2

a - d = 5 - 2 = 3

a = 5 ,

a + d = 5 + 2 = 7

3, 5 and 7


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