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. Observe the series: $$12, 19, 35, 59, 90, ?$$

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

3. Now, look at the pattern in the differences: $$7, 16, 24, 31$$

4. Calculate the differences between these differences:
   - $16 - 7 = 9$
   - $24 - 16 = 8$
   - $31 - 24 = 7$

5. The second-level differences are decreasing by 1 each time: $9, 8, 7, ...$

6. Following this pattern, the next second-level difference should be $6$.

7. Add this to the last first-level difference to get the next first-level difference:
   - $31 + 6 = 37$

8. Finally, add this to the last term in the series to find the next term:
   - $90 + 37 = 127$

**Answer:** $127$

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