24, 36, 72, 180, 550, 1890, 7560

Options

A. 24
B. 7560
C. 550
D. 180

Explanation

To solve the problem of identifying the incorrect number in the series: 24, 36, 72, 180, 550, 1890, 7560, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern
We need to find a consistent pattern in how the numbers are generated. Let's look at the ratios of consecutive terms.

- From 24 to 36:
\[ \frac{36}{24} = 1.5 \quad \text{(which is } 24 \times 1.5\text{)} \]

- From 36 to 72:
\[ \frac{72}{36} = 2 \quad \text{(which is } 36 \times 2\text{)} \]

- From 72 to 180:
\[ \frac{180}{72} = 2.5 \quad \text{(which is } 72 \times 2.5\text{)} \]

- From 180 to 550:
\[ \frac{550}{180} \approx 3.055 \quad \text{(not consistent with the pattern)} \]

### Step 2: Continue the pattern
If we continue the pattern, the next multiplication factor should be 3.

- From 180 to the next term:
\[ 180 \times 3 = 540 \]

### Step 3: Identify the incorrect number
The number that appears in the series after 180 is 550. Since we calculated that the next number should be 540, we can conclude that 550 is the incorrect number.

### Step 4: Verify the subsequent terms
To ensure the series continues correctly after replacing 550 with 540:

- From 540 to 1890:
\[ 540 \times 3.5 = 1890 \]

- From 1890 to 7560:
\[ 1890 \times 4 = 7560 \]

Both calculations confirm that the series maintains a consistent pattern after replacing 550 with 540.

### Conclusion
The incorrect number in the series is **550**.

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