Explanation:

Let's analyze the given sequence: $7, 11, 13, 17, 19, 23, 25, 29, ?$\nTo find the pattern, we calculate the differences between consecutive terms: $11 - 7 = 4$ $13 - 11 = 2$ $17 - 13 = 4$ $19 - 17 = 2$ $23 - 19 = 4$ $25 - 23 = 2$ $29 - 25 = 4$ \nThe sequence of differences is $4, 2, 4, 2, 4, 2, 4$. This is an alternating pattern where $4$ is added, then $2$ is added, and this cycle repeats.\nSince the last difference was $4$, the next difference in the pattern should be $2$. \nTo find the next term in the main sequence, we add this difference to the last known term:\nNext term $= 29 + 2 = 31$. \nLet's evaluate the options:\nOption (1) $37$: This would imply a difference of $37 - 29 = 8$, which does not fit the pattern.\nOption (2) $35$: This would imply a difference of $35 - 29 = 6$, which does not fit the pattern.\nOption (3) $31$: This matches our calculated next term, as $29 + 2 = 31$.\nOption (4) $33$: This would imply a difference of $33 - 29 = 4$. While $4$ is part of the pattern, it would break the alternating sequence ($4,2,4,2,4,2,4,\mathbf{4}$ instead of $4,2,4,2,4,2,4,\mathbf{2}$). Therefore, $33$ is incorrect. \nThus, the next term in the sequence is $31$. The correct option is (3) 31.