Find the next number in the series:

$$40, 66, 116, 198, 320, ?$$

Question

Find the next number in the series:

$$40, 66, 116, 198, 320, ?$$

Accepted Answer

**Solution:**

1. Observe the given series: $$40, 66, 116, 198, 320, ?$$

2. Calculate the differences between consecutive terms:
   - $66 - 40 = 26$
   - $116 - 66 = 50$
   - $198 - 116 = 82$
   - $320 - 198 = 122$

3. Now, examine the pattern in the differences:
   - $26, 50, 82, 122$

4. Calculate the differences between these differences:
   - $50 - 26 = 24$
   - $82 - 50 = 32$
   - $122 - 82 = 40$

5. The second-level differences are increasing by 8 each time:
   - $24, 32, 40, ...$

6. The next second-level difference should be $40 + 8 = 48$

7. Therefore, the next first-level difference is:
   - $122 + 48 = 170$

8. Finally, the next term in the series is:
   - $320 + 170 = 490$

**Answer:** $490$

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