This is the formula for the nth term in an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
d is the common difference and n is the number of terms.
This is the formula since an arithmetic sequence looks like this:
[tex]a_1,a_1+d,a_1+2d,...a_1+(n-1)d[/tex]
So:
[tex]a_6=a_1+(6-1)10 \\ 62=a_1+50 \\ 12=a_1[/tex]
Since we have the first term equal to 12 then:
[tex]a_{15}=a_1+(15-1)10 \\ a_{15}=12+140=152[/tex]
