Given `a_8=26, a_12=42`

The equation for an arithmetic sequence is

`a_n=a_1+(n-1)d`

`a_8=a_1+(8-1)d`

`26=a_1+7d`

Equation 1: `26=a_1+7d`

``

`a_n=a_1+(n-1)d`

`a_12=a_1+(12-1)d`

`42=a_1+11d`

Equation 2: `42=a_1+11d`

``

Using equation 1 and equation 2 solve for the `a_1` and `d` using the substitution method or the elimination method. The substitution method is shown below.

`26=a_1+7d`

`a_1=26-7d`

`42=a_1+11d`

`42=(26-7d)+11d`

`42-26=-7d+11d`

`16=6d`

`d=4`

`a_1=26-7d`

`a_1=26-7(4)`

`a_1=26-28`

`a_1=-2`

Find the equation of the arithmetic sequence using the `a_1` and `d` .

`a_n=a_1+(n-1)d`

`a_n=-2+(n-1)(4)`

`a_n=-2+4n-4`

`a_n=4n-6`

Find the first 5 terms of the sequence.

`a_n=4n-6`

`a_1=4(1)-6=4-6=-2`

`a_2=4(2)-6=8-6=2`

`a_3=4(3)-6=12-6=6`

`a_4=4(4)-6=16-6=10`

`a_5=4(5)-5=20-6=14`

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