Find the wrong number in the following number series questions.
100,142,212,310,436,595,772

Options

A. A)142
B. B)595
C. C)310
D. D)772

Answer

To find the wrong number in the given series: 100, 142, 212, 310, 436, 595, 772, we will analyze the pattern of differences between consecutive terms.

### Step-by-Step Solution:

1. **Identify the Terms:**
The series is:
- 1st term: 100
- 2nd term: 142
- 3rd term: 212
- 4th term: 310
- 5th term: 436
- 6th term: 595
- 7th term: 772

2. **Calculate the Differences:**
Let's calculate the differences between consecutive terms:
- Difference between 100 and 142:
\( 142 - 100 = 42 \)
- Difference between 142 and 212:
\( 212 - 142 = 70 \)
- Difference between 212 and 310:
\( 310 - 212 = 98 \)
- Difference between 310 and 436:
\( 436 - 310 = 126 \)
- Difference between 436 and 595:
\( 595 - 436 = 159 \)
- Difference between 595 and 772:
\( 772 - 595 = 177 \)

So, the differences are: 42, 70, 98, 126, 159, 177.

3. **Identify the Pattern in Differences:**
Now, let's look at the differences:
- From 42 to 70: Increase of \( 70 - 42 = 28 \)
- From 70 to 98: Increase of \( 98 - 70 = 28 \)
- From 98 to 126: Increase of \( 126 - 98 = 28 \)
- From 126 to 159: Increase of \( 159 - 126 = 33 \) (This is where the pattern breaks)
- From 159 to 177: Increase of \( 177 - 159 = 18 \)

The expected pattern should have continued with an increase of 28.

4. **Determine the Correct Value:**
Continuing the pattern:
- After 126, the next difference should be \( 126 + 28 = 154 \).
- Therefore, the next term after 436 should be:
\( 436 + 154 = 590 \).

5. **Identify the Wrong Number:**
The term we actually have is 595 instead of 590. Thus, 595 is the wrong number in the series.

### Conclusion:
The wrong number in the series is **595**.

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