Write the first six terms of an arithmetic sequence that has 12 for the first term and 42 for the sixth term

This is an arithmetic progression.

Tn  =  a + (n -1)* d.   

a = First term
n = number of terms
d = common difference.

First term, a = 12.
Sixth term, T6  =  a + (6 -1)*d =  a + 5d = 42
a + 5d = 42
12 + 5d = 42
5d = 42 - 12
5d = 30
d  = 30/5
d = 6.

Writing the first six terms, we keep adding six.
12, 18, 24, 30, 36, 42.
Cheers.