What will come in place of questions mark (?) in the following number series ?
`"656 344 188 110 ?"`

Options

A. 76
B. 79
C. 71
D. 73

Answer

To find the missing number in the series `656, 344, 188, 110, ?`, we will analyze the differences between consecutive terms.

### Step 1: Calculate the Differences
1. **First Difference:**
- \( 656 - 344 = 312 \)

2. **Second Difference:**
- \( 344 - 188 = 156 \)

3. **Third Difference:**
- \( 188 - 110 = 78 \)

### Step 2: Observe the Pattern in Differences
Now we have the differences:
- First difference: 312
- Second difference: 156
- Third difference: 78

### Step 3: Identify the Relationship
Notice that:
- \( 312 = 78 \times 4 \)
- \( 156 = 78 \times 2 \)
- \( 78 = 78 \times 1 \)

The pattern shows that the differences are multiples of 78:
- The first difference is \( 78 \times 4 \)
- The second difference is \( 78 \times 2 \)
- The third difference is \( 78 \times 1 \)

### Step 4: Determine the Next Difference
Following the pattern, the next difference should be:
- \( 78 \times 0.5 = 39 \)

### Step 5: Calculate the Missing Term
Now, we subtract this difference from the last known term (110):
- \( 110 - 39 = 71 \)

### Conclusion
The missing number in the series is **71**.

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