588 563 540 519 ? 483 468

Options

A. 500
B. 496
C. 494
D. 490

Explanation

To solve the series: 588, 563, 540, 519, ?, 483, 468, we need to identify the pattern in the differences between the numbers.

### Step-by-Step Solution:

1. **Identify the Differences**:
- Calculate the difference between consecutive terms:
- \( 588 - 563 = 25 \)
- \( 563 - 540 = 23 \)
- \( 540 - 519 = 21 \)

2. **Continue the Pattern**:
- The differences we have so far are: 25, 23, 21.
- Notice that these differences decrease by 2 each time:
- \( 25 - 2 = 23 \)
- \( 23 - 2 = 21 \)

3. **Find the Next Difference**:
- Continuing this pattern, the next difference should be:
- \( 21 - 2 = 19 \)

4. **Calculate the Missing Term**:
- Now, we can find the missing term in the series:
- \( 519 - 19 = 500 \)

5. **Verify the Next Differences**:
- To ensure our answer is correct, we can check the next term:
- The next term after 500 should be:
- \( 500 - 17 = 483 \) (since the next difference is \( 19 - 2 = 17 \))
- This confirms that the pattern holds.

6. **Final Confirmation**:
- The series now reads: 588, 563, 540, 519, **500**, 483, 468.
- The differences are: 25, 23, 21, 19, 17, which consistently decrease by 2.

### Conclusion:
The missing term in the series is **500**.