Find the wrong number in the following number series.
1201,1200,1197,1188,1161,1082,837

Options

A. 1200
B. 1188
C. 837
D. 1082

Answer

To find the wrong number in the series 1201, 1200, 1197, 1188, 1161, 1082, 837, we will analyze the differences between consecutive terms and look for a pattern.

### Step 1: Write down the series
The given series is:
- 1201
- 1200
- 1197
- 1188
- 1161
- 1082
- 837

### Step 2: Calculate the differences between consecutive terms
Let's find the differences:
- 1201 - 1200 = 1
- 1200 - 1197 = 3
- 1197 - 1188 = 9
- 1188 - 1161 = 27
- 1161 - 1082 = 79
- 1082 - 837 = 245

So, the differences are:
- 1, 3, 9, 27, 79, 245

### Step 3: Analyze the differences
Now, let's look for a pattern in the differences:
- The first three differences (1, 3, 9) are powers of 3:
- 1 = 3^0
- 3 = 3^1
- 9 = 3^2
- The next difference is 27, which is 3^3.
- However, the next difference is 79, which does not fit the pattern.

### Step 4: Identify the expected difference
Continuing the pattern, the next difference after 27 should be:
- 3^4 = 81

### Step 5: Find the wrong number
If we replace the difference of 79 with 81, we can find the correct term:
- The correct term after 1161 should be:
- 1161 - 81 = 1080

### Step 6: Conclusion
Thus, the wrong number in the series is 1082. The correct number should be 1080.

### Final Answer
The wrong number in the series is **1082**.

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