hello
to determine if the sequence is arthimetic or a geometric progression, we check if a common difference or common ratio exists between the two sequence
the sequence is 36, 30, 24, 18,......
from careful observation, this is an arthimetic progression because a common difference exists between them
d = 30 - 36 = -6
or
d = 24 - 30 = -6
to find the 67th term, let's apply the formula
[tex]\begin{gathered} T_n=a+(n-1)d \\ T_{67}=a+(67-1)d \\ a=\text{first term = 36} \\ d=common\text{ difference = }-6 \\ T_{67}=36+(67-1)\times-6 \\ T_{67}=36+66\times-6 \\ T_{67}=36-396 \\ T_{67}=-360 \end{gathered}[/tex]