1. **Stating the problem:** We are given the sequence 25, 32, 37, 47, 58, ? and need to find the next number. 2. **Analyze the differences between terms:** Calculate the differences between consecutive terms: $$32 - 25 = 7$$ $$37 - 32 = 5$$ $$47 - 37 = 10$$ $$58 - 47 = 11$$ 3. **Look for a pattern in the differences:** The differences are 7, 5, 10, 11. There is no immediately obvious arithmetic or geometric pattern. 4. **Check if differences of differences reveal a pattern:** Calculate second differences: $$5 - 7 = -2$$ $$10 - 5 = 5$$ $$11 - 10 = 1$$ Second differences are -2, 5, 1, which also do not form a clear pattern. 5. **Try to find a pattern in the original sequence:** Since differences are irregular, consider if the sequence could be formed by alternating patterns or other rules. 6. **Check odd and even terms separately:** - Odd terms: 25, 37, 58 - Even terms: 32, 47 Differences in odd terms: $$37 - 25 = 12$$ $$58 - 37 = 21$$ Differences in even terms: $$47 - 32 = 15$$ 7. **Predict next odd term difference:** The odd term differences increase by 9 (21 - 12 = 9), so next difference might be 21 + 9 = 30. 8. **Calculate next odd term:** $$58 + 30 = 88$$ 9. **Conclusion:** The next number in the sequence is likely **88**. **Final answer:** 88