Solution:
The arithmetic sequence is given below as
[tex]15,22,29,36[/tex]Step 1:
Calculate the common difference
[tex]\begin{gathered} d=t_2-t_1 \\ d=22-15 \\ d=7 \end{gathered}[/tex]Step 2:
The nth term of an arithmetic progression is given below as
[tex]\begin{gathered} T_n=a+(n-1)d \\ where, \\ a=15 \\ n=67 \\ d=7 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} T_{67}=15+(67-1)7 \\ T_{67}=15+66\times7 \\ T_{67}=15+463 \\ T_{67}=477 \end{gathered}[/tex]Hence,
The 67th term of the arithmetic sequence is
[tex]\Rightarrow477[/tex]