Answer:
[tex]a_n=6+12n[/tex]
Step-by-step explanation:
This is an arithmetic sequence, the kind where you start with a number (first term), then add a specific number (the common difference) to get the next term, and on and on like that.
1st term: 18
2nd term: 18 + 12 = 30
3rd term: 30 +12 = 42
4th term: 42 + 12 = 54, etc.
[tex]\vdots\\a_n=a_1+(n-1)d[/tex]
In this formula, n is the number of a term, and d is the common difference.
In this question, [tex]a_1=18 \text{ and } d=12[/tex], so
[tex]a_n=18+(n-1)12\\a_n=18+12n-12\\a_n=6+12n[/tex]
