Find the missing number in the series:

14, 20, 28, 39, ?, 74

Question

Find the missing number in the series:

14, 20, 28, 39, ?, 74

Accepted Answer

**Solution:**

1. Observe the differences between consecutive terms:
   - $20 - 14 = 6$
   - $28 - 20 = 8$
   - $39 - 28 = 11$

2. The differences are increasing but not by a fixed amount. Let's check the pattern of differences:
   - From 6 to 8: increase by 2
   - From 8 to 11: increase by 3

3. Following this pattern, the next increase should be by 4:
   - Next difference = $11 + 4 = 15$

4. Therefore, the missing term is:
   - $39 + 15 = 54$

5. To verify, check the difference between the next known term and the missing term:
   - $74 - 54 = 20$

6. The differences are: 6, 8, 11, 15, 20 which follow an increasing pattern.

**Answer:** $54$

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