The numbers of the sequence 56,72,90,110,132,154 form a pattern. Which of term is a misfit in the pattern

Options

A. 72
B. 110
C. 132
D. 154

Answer

To determine which term in the sequence 56, 72, 90, 110, 132, 154 is a misfit, we will analyze the differences between consecutive terms and look for a consistent pattern.

### Step-by-Step Solution:

1. **List the Sequence**:
The given sequence is:
\[ 56, 72, 90, 110, 132, 154 \]

2. **Calculate the Differences**:
We will find the difference between each consecutive term:
- \(72 - 56 = 16\)
- \(90 - 72 = 18\)
- \(110 - 90 = 20\)
- \(132 - 110 = 22\)
- \(154 - 132 = 22\)

So, the differences are:
\[ 16, 18, 20, 22, 22 \]

3. **Analyze the Differences**:
Now, let's analyze the differences:
- The first difference is 16.
- The second difference is 18 (which is 16 + 2).
- The third difference is 20 (which is 18 + 2).
- The fourth difference is 22 (which is 20 + 2).
- The fifth difference is also 22.

4. **Identify the Pattern**:
The expected pattern is that the differences should increase consistently by 2. However, the last difference does not follow this pattern since it remains 22 instead of increasing to 24.

5. **Identify the Misfit**:
Since the difference from 132 to 154 should have been 24 (following the pattern), but it is only 22, we can conclude that 154 is the misfit in the sequence.

### Conclusion:
The term that does not fit the pattern is **154**.

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