S5 = 20
A6 = 25
A1=
d=
The general formula for arithmetic sequence is:
An = A1 + (n - 1)d
25 = A1 + 6d - d (1)
And the formula for arithmetic sum:
Sn = n(A1 + An)/2
20 = 5(A1 + 25 - d)/2
8 = A1 + 25 - d (2)
We have a system of two equations with two variables.
25 = A1 + 5d
8 = A1 + 25 - d
For both equations, we can solve for d and then equal both equations as follows:
5 - A1/5 = d (1)
A1 + 17 = d (2)
A1 + 17 = 5 - A1/5
A1 = -10.
Now we just replace the value of A1 in equation 1:
d = 7
