Find the next number in the series:

$$15, 21, 38, 65, 101, ?$$

Question

Find the next number in the series:

$$15, 21, 38, 65, 101, ?$$

Accepted Answer

**Solution:**

1. Observe the series: $15, 21, 38, 65, 101, ?$

2. Calculate the differences between consecutive terms:
   - $21 - 15 = 6$
   - $38 - 21 = 17$
   - $65 - 38 = 27$
   - $101 - 65 = 36$

3. Look at the pattern in the differences: $6, 17, 27, 36$

4. Calculate the differences of these differences:
   - $17 - 6 = 11$
   - $27 - 17 = 10$
   - $36 - 27 = 9$

5. The second-level differences are decreasing by 1 each time: $11, 10, 9, ...$

6. Next second-level difference should be $8$.

7. So, next first-level difference = $36 + 8 = 44$

8. Therefore, next term = $101 + 44 = 145$

**Answer:** $145$

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