What will be come in place of the question mark (?) in the given number series
700 457 376 349 340 ?

Options

A. 266
B. 329
C. 304
D. 337

Answer

To solve the number series question, we will analyze the differences between the consecutive numbers and identify a pattern.

Given series:
700, 457, 376, 349, 340, ?

**Step 1: Find the differences between consecutive numbers.**

1. Calculate the difference between the first two numbers:
\( 700 - 457 = 243 \)

2. Calculate the difference between the second and third numbers:
\( 457 - 376 = 81 \)

3. Calculate the difference between the third and fourth numbers:
\( 376 - 349 = 27 \)

4. Calculate the difference between the fourth and fifth numbers:
\( 349 - 340 = 9 \)

Now we have the differences:
- 243
- 81
- 27
- 9

**Step 2: Identify the pattern in the differences.**

The differences we calculated are:
- 243, which is \( 3^5 \)
- 81, which is \( 3^4 \)
- 27, which is \( 3^3 \)
- 9, which is \( 3^2 \)

We can see that the differences are powers of 3, decreasing by 1 in the exponent each time.

**Step 3: Determine the next difference.**

Following the pattern, the next difference should be:
- \( 3^1 = 3 \)

**Step 4: Calculate the next number in the series.**

Since the series is decreasing, we subtract the next difference from the last number in the series:
- \( 340 - 3 = 337 \)

Thus, the number that will come in place of the question mark (?) is **337**.

**Final Answer: 337**

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