# The sum of the three terms in a. p. in 15 and sum of their squares is93. find the numbers.

2
by gite

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by gite

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3f+3d=15

f+d=5

(5-d)²+5²+(5+d)²=93

25+25+25+d²+d²+10d-10d=93

75+2d²=93

2d²=93-75=18

d²=9

d= postive 3 or -ve 3

numbers=2,5,8...

or 8,5,2

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Sum = 15

a-d +a+a+d = 15 ⇒ 3a = 15 ⇒ a = 5

Sum of their squares = 93

(a-d)² + a² + (a+d)² = 93

a² + d² + a² + a² + d² = 93

25 + 2d² + 25 + 25 = 93

2d² = 18

d² = 9

d = 3 or d = -3

the terms when a = 5, d = 3 are

2, 5, 8

the terms when a = 5 , d = -3 are

8, 5, 2