In each of the following questions, find the wrong term in the given series.
102,83,66,50,38,27,18

Options

A. 102
B. 83
C. 38
D. 50

Answer

To find the wrong term in the series: 102, 83, 66, 50, 38, 27, 18, we will analyze the pattern of the series step by step.

### Step 1: Identify the Pattern
We will look for a consistent pattern in the series. One common approach is to examine the differences between consecutive terms.

### Step 2: Calculate the Differences
Let's calculate the differences between the terms:

- 102 - 83 = 19
- 83 - 66 = 17
- 66 - 50 = 16
- 50 - 38 = 12
- 38 - 27 = 11
- 27 - 18 = 9

The differences are: 19, 17, 16, 12, 11, 9.

### Step 3: Look for a Consistent Decrease
The differences do not show a consistent pattern. However, we can observe that the differences are decreasing, but not uniformly.

### Step 4: Check for a Square Pattern
Next, let's check if there's a pattern involving squares of integers.

- 10² + 2 = 100 + 2 = 102
- 9² + 2 = 81 + 2 = 83
- 8² + 2 = 64 + 2 = 66
- 7² + 2 = 49 + 2 = 51 (but we have 50)
- 6² + 2 = 36 + 2 = 38
- 5² + 2 = 25 + 2 = 27
- 4² + 2 = 16 + 2 = 18

### Step 5: Identify the Wrong Term
From the calculations, we see that for the term 50, it should actually be 51 according to the pattern of squares. Therefore, 50 is the wrong term in the series.

### Conclusion
The wrong term in the series is **50**.

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