I need help regarding the following question:
Four different integers are in A.P. One of these integers is equal to the squares of the rest integers. Find the numbers.
It is like this:
If a, b, c, d are in A.P. then d=a^2 +b^2 +c^2
I know the answer, but I simply can't figure out the explanation. The A.P. is -1,0,1,2
But I do not understand how it came.
Any help will be appreciated.
2b=a+c --- 1
b=2c-d --- 2
Sub 2 into 1, 2(2c-d)=a+c
a=3c-2d -- 3
Substitute 3 and 2 into 4
After simplifying, you are left with
Then let c be 0(you could have picked d to be 0), then solve for d and the rest of the unknowns.