180, 271, 352, 423, 484, 535, ?

Options

A. 576
B. 577
C. 578
D. 579

Explanation

To find the missing number in the series: 180, 271, 352, 423, 484, 535, ?, we will analyze the pattern in the differences between consecutive terms.

### Step-by-Step Solution:

1. **Identify the Series**:
The given series is:
180, 271, 352, 423, 484, 535.

2. **Calculate the Differences**:
We will calculate the differences between consecutive terms:
- 271 - 180 = 91
- 352 - 271 = 81
- 423 - 352 = 71
- 484 - 423 = 61
- 535 - 484 = 51

So, the differences are:
91, 81, 71, 61, 51.

3. **Identify the Pattern in Differences**:
The differences form a decreasing pattern:
- 91, 81, 71, 61, 51.
Each difference decreases by 10.

4. **Find the Next Difference**:
Continuing the pattern, the next difference should be:
51 - 10 = 41.

5. **Calculate the Next Term**:
Now, we add this difference to the last term in the series:
535 + 41 = 576.

6. **Conclusion**:
The missing number in the series is **576**.

### Summary of the Steps:
- Identify the series.
- Calculate the differences between consecutive terms.
- Identify the pattern in the differences.
- Calculate the next difference.
- Add the next difference to the last term to find the missing number.