Find the missing number in the series:

138, 210, 66, 282, -6, ?

Question

Find the missing number in the series:

138, 210, 66, 282, -6, ?

Accepted Answer

**Solution:**

1. Observe the series: 138, 210, 66, 282, -6, ?

2. Look at the pattern between alternate terms:
   - From 138 to 66: 138 - 72 = 66
   - From 210 to 282: 210 + 72 = 282
   - From 66 to -6: 66 - 72 = -6

3. The pattern alternates between subtracting and adding 72:
   - 138 (start)
   - 210 (138 + 72)
   - 66 (210 - 144) ? This doesn't fit, so check another approach.

4. Try to analyze differences between consecutive terms:
   - 210 - 138 = 72
   - 66 - 210 = -144
   - 282 - 66 = 216
   - (-6) - 282 = -288

5. The differences are: +72, -144, +216, -288
   - These differences increase by 72 each time, alternating signs.

6. Next difference should be +360 (since 72, 144, 216, 288, 360)

7. Therefore, next term = -6 + 360 = 354

**Answer:** 354

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