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Let x be the very central point for the given 4 terms of the AP.
In other words, let x be the average of the 4 terms of the AP
x = .
Next, let d be the common difference of the AP.
Our goal is to find "x" and "d".
It is clear that
= x - 1.5d;
= x - 0.5d;
= x + 0.5d;
= x + 1.5d.
Therefore, + = 2x.
It implies 2x = 8, and hence x = 4.
Also, = 15.
It implies (x-0.5d)*(x+0.5d) = 15, or
x^2 - 0.25d^2 = 15.
Substitute here x= 4 to get
0.25d^2 = 4^2 - 15 = 16 - 15 = 1.
Thus d^2 = = 4; hence, d = = +/- 2.
The problem is just solved. We know the central point x = 4 and the common difference d = +/-2.
If d = 2, then = 4-1.5*2 = 1; = 1+2 = 3; = 3+2 = 5, and = 5 + 2 = 7.
If d = -2, then we have the same sequence in the REVERSED order: = 7; = 5; = 3 and = 1.
Solved.