Find the next number in the series:

$$2, 6, 12, 20, 30, ?$$

Question

Find the next number in the series:

$$2, 6, 12, 20, 30, ?$$

Accepted Answer

**Solution:**

1. Observe the given series: $$2, 6, 12, 20, 30, ?$$

2. Calculate the difference between consecutive terms:
   - $6 - 2 = 4$
   - $12 - 6 = 6$
   - $20 - 12 = 8$
   - $30 - 20 = 10$

3. The differences form the sequence: $$4, 6, 8, 10$$ which increases by 2 each time.

4. The next difference should be $$10 + 2 = 12$$.

5. Add this to the last term:
   $$30 + 12 = 42$$

**Answer:** $42$

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Answer

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