17, 21, 37, 73, 137, 237, ….

Options

A. 363
B. 369
C. 375
D. 381

Explanation

To solve the series: 17, 21, 37, 73, 137, 237, ..., we need to identify the pattern in the differences between the consecutive terms.

### Step-by-Step Solution:

1. **Identify the first term and the second term:**
- The first term is 17.
- The second term is 21.

2. **Calculate the difference between the first and second terms:**
- Difference = 21 - 17 = 4.

3. **Identify the second and third terms:**
- The second term is 21.
- The third term is 37.

4. **Calculate the difference between the second and third terms:**
- Difference = 37 - 21 = 16.

5. **Identify the third and fourth terms:**
- The third term is 37.
- The fourth term is 73.

6. **Calculate the difference between the third and fourth terms:**
- Difference = 73 - 37 = 36.

7. **Identify the fourth and fifth terms:**
- The fourth term is 73.
- The fifth term is 137.

8. **Calculate the difference between the fourth and fifth terms:**
- Difference = 137 - 73 = 64.

9. **Identify the fifth and sixth terms:**
- The fifth term is 137.
- The sixth term is 237.

10. **Calculate the difference between the fifth and sixth terms:**
- Difference = 237 - 137 = 100.

11. **Now, let's summarize the differences:**
- The differences are: 4, 16, 36, 64, 100.

12. **Notice the pattern in the differences:**
- 4 = 2²
- 16 = 4²
- 36 = 6²
- 64 = 8²
- 100 = 10²

13. **Continue the pattern:**
- The next difference should be the square of the next even number, which is 12.
- 12² = 144.

14. **Add this difference to the last term in the series:**
- Next term = 237 + 144 = 381.

15. **Final answer:**
- The next term in the series is 381.