Answer:
[tex]a_n=33+6n[/tex]
Step-by-step explanation:
General form of arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
Given terms:
- [tex]a_1=39[/tex]
- [tex]a_2=45[/tex]
- [tex]a_3=51[/tex]
To find the common difference, subtract a term from the next:
[tex]d=a_3-a_2=51-45=6[/tex]
Substitute [tex]a=39[/tex] and [tex]d=6[/tex] into the formula:
[tex]\implies a_n=39+6(n-1)[/tex]
[tex]\implies a_n=39+6n-6[/tex]
[tex]\implies a_n=33+6n[/tex]
