Question

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

Answer 1

f+f+d+f+2d=15
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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Answer 2

Let the three terms of AP be a-d, a, a+d
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