Precalculus, Chapter 9, 9.2, Section 9.2, Problem 37

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