456.5, 407, 368.5, 341, 324.5 ?

Options

A. 321
B. 319
C. 317
D. 323

Explanation

To find the missing number in the series: 456.5, 407, 368.5, 341, 324.5, we will analyze the differences between the consecutive terms.

**Step 1: Calculate the differences between consecutive terms.**

- Difference between 456.5 and 407:
\[ 456.5 - 407 = 49.5 \]

- Difference between 407 and 368.5:
\[ 407 - 368.5 = 38.5 \]

- Difference between 368.5 and 341:
\[ 368.5 - 341 = 27.5 \]

- Difference between 341 and 324.5:
\[ 341 - 324.5 = 16.5 \]

**Step 2: List the differences obtained.**
The differences are:
- 49.5
- 38.5
- 27.5
- 16.5

**Step 3: Calculate the differences of the differences.**
Now, we will find the differences of these differences:
- Difference between 49.5 and 38.5:
\[ 49.5 - 38.5 = 11 \]

- Difference between 38.5 and 27.5:
\[ 38.5 - 27.5 = 11 \]

- Difference between 27.5 and 16.5:
\[ 27.5 - 16.5 = 11 \]

**Step 4: Identify the pattern.**
We observe that the second differences are constant at 11. This indicates that the differences are decreasing by a consistent amount.

**Step 5: Determine the next difference.**
Since the last difference we calculated was 16.5, we subtract 11 from it to find the next difference:
\[ 16.5 - 11 = 5.5 \]

**Step 6: Calculate the next term in the series.**
Now, we subtract this new difference (5.5) from the last known term (324.5):
\[ 324.5 - 5.5 = 319 \]

Thus, the missing number in the series is **319**.

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