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

2. The pattern of differences is: $+6, +17, +27, +36, +44...$
   - The increments between differences are: $17 - 6 = 11$, $27 - 17 = 10$, $36 - 27 = 9$, which suggests a decreasing increment by 1 each time.

3. Next difference should be $44$ (following the pattern).

4. Add $44$ to the last term:
   $$101 + 44 = 145$$

**Answer:** $145$

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