The first term of the arithmetic progression is 161, and the second term is 154. The common difference, d, is given by:

\(d = 154 - 161 = -7\)

The sum of the first m terms of an arithmetic progression is given by the formula:

\(S_m = \frac{m}{2} (2a + (m-1)d)\)

Substituting the given values, we have:

\(S_m = \frac{m}{2} (2 \times 161 + (m-1)(-7)) = 0\)

Simplifying inside the brackets:

\(2 \times 161 = 322\)

Thus, the equation becomes:

\(\frac{m}{2} (322 + (m-1)(-7)) = 0\)

Solving for m:

\(322 + (m-1)(-7) = 0\)

\(322 - 7m + 7 = 0\)

\(329 - 7m = 0\)

\(7m = 329\)

\(m = \frac{329}{7} = 47\)