Question

The sum of first three terms is an arithmetic progression is 24 and the sum of their square is 224 find the first three terms of arithmetic progression​

Answer 1

Answer:4, 8, 12

Step-by-step explanation:

Sum of first three terms is three times the middle number, which is the second term

So the second term is 24/3=8

So the numbers can be written as 8-d, 8 and 8+d where d is the common diffu

Sum of squs is 224

So (8-d)^2 + 8^2 + (8+d)^2 =224

We know that (a-b)^2 + (a+b)^2=2(a^2+b^2)

So 2(8^2 + d^2) + 8^2 =224

2d^2 +192=224

2d^2= 32

d^2=16

d=+4 or -4

If d is 4, the terms are 4, 8 and 12

If d is -4, the terms are 12, 8 and 4