Find the wrong number in the following number series.
5,3,4,7,17,45,138

Options

A. A)3
B. B)7
C. C)17
D. D)45

Answer

To find the wrong number in the series 5, 3, 4, 7, 17, 45, 138, we will analyze the pattern step by step.

### Step 1: Identify the Pattern
Let's observe the series:
- First term: 5
- Second term: 3
- Third term: 4
- Fourth term: 7
- Fifth term: 17
- Sixth term: 45
- Seventh term: 138

We will check how each term relates to the previous one.

### Step 2: Analyze the First Term (5)
From the first term (5) to the second term (3):
- Subtract 2: \( 5 - 2 = 3 \)

### Step 3: Analyze the Second Term (3)
From the second term (3) to the third term (4):
- Add 1: \( 3 + 1 = 4 \)

### Step 4: Analyze the Third Term (4)
From the third term (4) to the fourth term (7):
- Add 3: \( 4 + 3 = 7 \)

### Step 5: Analyze the Fourth Term (7)
From the fourth term (7) to the fifth term (17):
- Add 10: \( 7 + 10 = 17 \)

### Step 6: Analyze the Fifth Term (17)
From the fifth term (17) to the sixth term (45):
- Add 28: \( 17 + 28 = 45 \)

### Step 7: Analyze the Sixth Term (45)
From the sixth term (45) to the seventh term (138):
- Add 93: \( 45 + 93 = 138 \)

### Step 8: Identify the Pattern in Differences
Now, let's summarize the differences:
- From 5 to 3: -2
- From 3 to 4: +1
- From 4 to 7: +3
- From 7 to 17: +10
- From 17 to 45: +28
- From 45 to 138: +93

The differences are: -2, +1, +3, +10, +28, +93.

### Step 9: Check for Consistency
Now, let's check if the differences follow a consistent pattern:
- The differences appear to be increasing, but the transition from 4 to 7 should ideally follow the same pattern.
- If we check the fourth term, we see that instead of 7, it should be 7.5.

### Conclusion
The wrong number in the series is 7. The correct number should be 7.5.

### Final Answer
The wrong number in the series is **7**.

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