Which term in the arithmetic sequence $9,4,-1, \ldots$ has the value $-146 ?$

Step 1 ：Given the arithmetic sequence: \(9, 4, -1, \ldots\)

Step 2 ：Find the common difference (d): \(d = 4 - 9 = -5\)

Step 3 ：Use the formula for the nth term of an arithmetic sequence: \(a_n = a_1 + (n - 1)d\)

Step 4 ：Plug in the given value for the nth term (\(-146\)) and the known values for \(a_1\) and d: \(-146 = 9 + (n - 1)(-5)\)

Step 5 ：Solve for n: \(n = 32\)

Step 6 ：\(\boxed{32}\) is the term number in the sequence with the value \(-146\)