3, 7, 13, 21, 31, ….

Options

A. 40
B. 41
C. 42
D. 43

Explanation

To find the next number in the series 3, 7, 13, 21, 31, we will analyze the pattern of the series step by step.

**Step 1: Identify the differences between consecutive terms.**
- The first term is 3.
- The second term is 7. The difference is 7 - 3 = 4.
- The third term is 13. The difference is 13 - 7 = 6.
- The fourth term is 21. The difference is 21 - 13 = 8.
- The fifth term is 31. The difference is 31 - 21 = 10.

**Step 2: List the differences.**
- The differences we found are: 4, 6, 8, 10.

**Step 3: Identify the pattern in the differences.**
- The differences are increasing by 2 each time:
- 4 (first difference)
- 6 (second difference, which is 4 + 2)
- 8 (third difference, which is 6 + 2)
- 10 (fourth difference, which is 8 + 2)

**Step 4: Determine the next difference.**
- Following the pattern, the next difference should be 10 + 2 = 12.

**Step 5: Add the next difference to the last term in the series.**
- The last term we have is 31.
- So, we will add the next difference (12) to it:
- 31 + 12 = 43.

**Step 6: Conclusion**
- Therefore, the next number in the series is **43**.