Find the next number in the series:

12, 19, 35, 59, 90, ?

Question

Find the next number in the series:

12, 19, 35, 59, 90, ?

Accepted Answer

**Solution:**

1. Analyze the differences between consecutive terms:
   - $19 - 12 = 7$
   - $35 - 19 = 16$
   - $59 - 35 = 24$
   - $90 - 59 = 31$

2. Differences are: $7, 16, 24, 31$

3. Find the differences between these differences:
   - $16 - 7 = 9$
   - $24 - 16 = 8$
   - $31 - 24 = 7$

4. The second-level differences are decreasing by 1:
   - $9, 8, 7, 6, ...$

5. Next difference should be:
   - $31 + 6 = 37$

6. Therefore, next term:
   - $90 + 37 = 127$

**Answer:** $127$

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