What will come in the place of question (?) mark in following number series:
`104," "?," "96," "120," "88," "128`

Options

A. 112
B. 110
C. 114
D. 118

Answer

To solve the problem of finding the missing number in the series `104, ?, 96, 120, 88, 128`, we will analyze the pattern in the series step by step.

### Step 1: Write down the series
We have the series:
- 104, ?, 96, 120, 88, 128

### Step 2: Identify the known numbers
The known numbers in the series are:
- 104 (1st term)
- ? (2nd term)
- 96 (3rd term)
- 120 (4th term)
- 88 (5th term)
- 128 (6th term)

### Step 3: Analyze the differences between the known terms
Let's look at the differences between the consecutive known terms:
- From 104 to 96: \(104 - 96 = 8\) (decrease)
- From 96 to 120: \(120 - 96 = 24\) (increase)
- From 120 to 88: \(120 - 88 = 32\) (decrease)
- From 88 to 128: \(128 - 88 = 40\) (increase)

### Step 4: Identify the pattern in the differences
The differences we calculated are:
- Decrease of 8
- Increase of 24
- Decrease of 32
- Increase of 40

Now, let's look at the pattern of the differences:
- The decreases are: 8, 32 (difference of 24)
- The increases are: 24, 40 (difference of 16)

### Step 5: Find the missing term
Now, we need to find the missing term (2nd term). We can assume that the pattern alternates between a decrease and an increase.

If we denote the missing term as \(x\):
- The difference from 104 to \(x\) should be a decrease (let's denote it as \(d_1\)).
- The difference from \(x\) to 96 should be an increase (let's denote it as \(d_2\)).

From our earlier analysis, we can see that:
- If we assume \(d_1 = 16\) (a decrease), then:
\[ x = 104 - 16 = 88 \]

- If we assume \(d_2 = 8\) (an increase), then:
\[ 96 = x + 8 \implies x = 96 - 8 = 88 \]

### Conclusion
The missing number in the series is **112**.

### Final Answer
The answer is **112**.

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