What will be the next number of the series:
3, 6, 10.5, 17, 26, ?

Question

What will be the next number of the series:  
3, 6, 10.5, 17, 26, ?

Accepted Answer

To find the next number in the series, analyze the pattern of differences between consecutive terms:

1. **Differences between terms:**  
   - $$6 - 3 = 3$$  
   - $$10.5 - 6 = 4.5$$  
   - $$17 - 10.5 = 6.5$$  
   - $$26 - 17 = 9$$

2. **Second-level differences (difference of differences):**  
   - $$4.5 - 3 = 1.5$$  
   - $$6.5 - 4.5 = 2$$  
   - $$9 - 6.5 = 2.5$$

The second-level differences increase by $$0.5$$. The next second-level difference will be $$3$$.

3. **Next first-level difference:**  
   Add $$3$$ to the last first-level difference ($$9$$):  
   $$9 + 3 = 12$$.

4. **Next term in the series:**  
   Add this difference ($$12$$) to the last term ($$26$$):  
   $$26 + 12 = 38$$.

Thus, the next number in the series is **38**, making option **(2)** correct.

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