What will come in place of (?) in the following number series?
112,?,166,238,382,670

Options

A. A)152
B. B)135
C. C)144
D. D)130

Answer

To find the missing term in the number series: 112, ?, 166, 238, 382, 670, we can analyze the differences between the terms.

### Step-by-Step Solution:

1. **List the given terms**:
- The series is: 112, ?, 166, 238, 382, 670.

2. **Identify the known terms**:
- The known terms are 112, 166, 238, 382, and 670.

3. **Calculate the differences between the known terms**:
- From 670 to 382:
\[ 670 - 382 = 288 \]
- From 382 to 238:
\[ 382 - 238 = 144 \]
- From 238 to 166:
\[ 238 - 166 = 72 \]

4. **Observe the pattern in the differences**:
- The differences are: 288, 144, 72.
- Notice that each difference is half of the previous one:
- \(288 \div 2 = 144\)
- \(144 \div 2 = 72\)

5. **Continue the pattern to find the next difference**:
- Following the pattern, the next difference should be:
\[ 72 \div 2 = 36 \]

6. **Calculate the missing term**:
- Since the difference before the term we are looking for is 36, we can find the missing term by subtracting 36 from 166:
\[ 166 - 36 = 130 \]

7. **Verify the next difference**:
- The difference after the missing term should be:
\[ 36 \div 2 = 18 \]
- Thus, the term before 112 should be:
\[ 112 + 18 = 130 \]

8. **Final answer**:
- Therefore, the missing term is **130**.