Find the wrong term in the following number series questions.
-5,10,-15,30,-45, 90,-180`

Options

A. `-10`
B. `30`
C. `-180`
D. `-45`

Answer

To find the wrong term in the series -5, 10, -15, 30, -45, 90, -180, we can analyze the pattern of the series step by step.

### Step 1: Identify the Pattern
The series alternates between negative and positive numbers:
- The first term is -5 (negative)
- The second term is 10 (positive)
- The third term is -15 (negative)
- The fourth term is 30 (positive)
- The fifth term is -45 (negative)
- The sixth term is 90 (positive)
- The seventh term is -180 (negative)

### Step 2: Determine the Multiplication Factor
Next, we observe how each term relates to the previous term:
- From -5 to 10: \(-5 \times -2 = 10\)
- From 10 to -15: \(10 \times -1.5 = -15\)
- From -15 to 30: \(-15 \times -2 = 30\)
- From 30 to -45: \(30 \times -1.5 = -45\)
- From -45 to 90: \(-45 \times -2 = 90\)
- From 90 to -180: \(90 \times -2 = -180\)

### Step 3: Check the Multiplication Consistency
We can see that the pattern alternates between multiplying by -2 and -1.5:
- Multiply by -2: \(-5 \to 10\), \(-15 \to 30\), \(-45 \to 90\)
- Multiply by -1.5: \(10 \to -15\), \(30 \to -45\), \(90 \to -180\)

### Step 4: Identify the Incorrect Term
Now, we check the multiplication for the term after -45:
- According to the pattern, \(-45\) should multiply by -2 to give \(90\), which is correct.
- However, when we multiply -45 by -1.5, we should get:
\[ -45 \times -1.5 = 67.5 \]
This means that the term after -45 should be 67.5, not 90.

### Conclusion
Thus, the wrong term in the series is **90**. The correct term should be **67.5**.