What should come in place of question mark (?) in the following number series ?
`"14 33 76 167 ? 733"`

Options

A. 345
B. 348
C. 351
D. 354

Answer

To find the missing number in the series: 14, 33, 76, 167, ?, 733, we can analyze the pattern of the series step by step.

### Step 1: Identify the pattern
We will look at how each number relates to the previous one.

1. From 14 to 33:
- \( 14 \times 2 + 5 = 33 \)

2. From 33 to 76:
- \( 33 \times 2 + 10 = 76 \)

3. From 76 to 167:
- \( 76 \times 2 + 15 = 167 \)

### Step 2: Establish the formula
From the calculations, we can see a pattern emerging:
- The multiplier is consistently 2.
- The additive constant appears to increase by 5 each time:
- From 5 to 10 (increased by 5)
- From 10 to 15 (increased by 5)

### Step 3: Predict the next number
Continuing this pattern, the next additive constant should be:
- \( 15 + 5 = 20 \)

So, we can calculate the next number in the series:
- \( 167 \times 2 + 20 \)

### Step 4: Perform the calculation
Now, let's perform the calculation:
- \( 167 \times 2 = 334 \)
- \( 334 + 20 = 354 \)

Thus, the missing number in the series is **354**.

### Step 5: Verify the next number
To ensure the pattern holds, let's check the next number after 354:
- \( 354 \times 2 + 25 \) (since the next additive constant is 25)
- \( 354 \times 2 = 708 \)
- \( 708 + 25 = 733 \)

This confirms that our pattern is consistent.

### Final Answer
The missing number is **354**.

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