The given sequence is 460, 451, 442,...
Let's subtract to find the difference in the sequence.
[tex]451-460=-9[/tex]
The difference is -9 (d = -9).
Let's use the formula for arithmetic sequences to find the 37th term (n = 37).
[tex]a_n=a_1+(n-1)d[/tex]
Where a1 = 460, n = 37, and d = -9.
[tex]\begin{gathered} a_{37}=460+(37-1)\cdot(-9) \\ a_{37}=460+(36)(-9) \\ a_{37}=460-324 \\ a_{37}=136 \end{gathered}[/tex]
Therefore, the 37th term is 136.
