Question

Find three numbers in Ap whose sum is 30 and sum of their squares is 308

Answer 1

Answer:

hey mate

Step-by-step explanation:

Let three numbers of AP be a+d, a ,and a-d

now according to question

sum of these terms is 18 so,

= (a+d)+(a)+(a-d)= 18

= a+d+a+a-d= 18

= 3a= 18

a= 18/3

= a= 6........(1)

second situation given in question

sum their squares is 180

(a+d)²+(a)²+(a-d)²= 180

= (a²+d²+2ad)+(a²)+(a²+d²-2ad)= 180

= a²+d²+2ad+a²+a²+d²-2ad=180

=3a²+2d²=180

= 3(6)²+2d²=180.......(putting a=6 from (1))

= 108+2d²= 180

=2d²= 180-108

2d²= 72

= d²= 36

d= +6 or -6

So there are 2 sets of three terms

first where a= 6 and d= -6

putting values in a+d, a, and a-d

three terms= 0,6,12

second when a= 6 and d=+6

putting values in a+d, a, and a-d

three terms= 12, 6, 0

hope this helps you

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