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.

Answer 1

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

3a = 15

a = $\frac{15}{3}$

a = 5

Sum of the extremes = 58

${(a-d)}^2$ + ${(a+d)}^2$ = 58

2( $a^2$ + $d^2$ ) = 58

$a^2$ + $d^2$ = 29

$5^2$ + $d^2$ = 29 [ since a = 5 ]

$d^2$ = 29 - 25

$d^2$ = 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