Find the wrong number in the following number series questions.
72,80,144,360,864,1872,3600

Options

A. 360
B. 144
C. 80
D. 864

Answer

To find the wrong number in the series: 72, 80, 144, 360, 864, 1872, 3600, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern in the series
We will look for a pattern in the differences or relationships between the numbers.

- From 72 to 80, the difference is 8.
- From 80 to 144, the difference is 64.
- From 144 to 360, the difference is 216.
- From 360 to 864, the difference is 504.
- From 864 to 1872, the difference is 1008.
- From 1872 to 3600, the difference is 1728.

### Step 2: Check for cubes in the differences
Now, we will check if these differences correspond to cubes of integers:

- The difference from 72 to 80 is \(2^3 = 8\).
- The difference from 80 to 144 is \(4^3 = 64\).
- The difference from 144 to 360 is \(6^3 = 216\).
- The difference from 360 to 864 should be \(8^3 = 512\) but is actually 504.
- The difference from 864 to 1872 is \(10^3 = 1000\) but is actually 1008.
- The difference from 1872 to 3600 is \(12^3 = 1728\).

### Step 3: Identify the discrepancy
We notice that the difference from 360 to 864 is supposed to be \(8^3 = 512\) but is actually 504. This indicates that there is a discrepancy in the number 864.

### Step 4: Calculate the correct number
If we add 512 to 360, we get:
\[ 360 + 512 = 872 \]

### Step 5: Conclusion
Thus, the wrong number in the series is 864, and it should be replaced with 872.

### Final Answer
The wrong number in the series is **864**.

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