The nnth term of an arithemtic progression with a1 as the first term and dd as the common difference is given by:

an=a1+(n−1)d

Using the 4th term, we write one equation:

a4=a1+(4−1)d

4=a1+3d(1)

Using the 8th term, we write one equation:

a8=a1+(8−1)d

22=a1+7d(2)

Subtract each side of (1) and (2) and solve for dd:

−18=−4d

4.5=d

Solve for a1 using (1):

4=a1+3(4.5)

4=a1+13.5

−9.5=a1

The first term is −9.5.

an=a1+(n−1)d

Using the 4th term, we write one equation:

a4=a1+(4−1)d

4=a1+3d(1)

Using the 8th term, we write one equation:

a8=a1+(8−1)d

22=a1+7d(2)

Subtract each side of (1) and (2) and solve for dd:

−18=−4d

4.5=d

Solve for a1 using (1):

4=a1+3(4.5)

4=a1+13.5

−9.5=a1

The first term is −9.5.