5, 15, 65, 315, ?

Options

A. 1556
B. 1565
C. 1665
D. 1656

Explanation

To find the missing number in the series: 5, 15, 65, 315, ?, we can follow these steps:

### Step 1: Identify the pattern
We start with the first number, which is 5. We need to find a consistent operation that transforms each number into the next.

### Step 2: Analyze the transitions
- From 5 to 15:
- We can multiply 5 by 5 and then subtract 10:
\[ 5 \times 5 - 10 = 25 - 10 = 15 \]

- From 15 to 65:
- Similarly, we multiply 15 by 5 and then subtract 10:
\[ 15 \times 5 - 10 = 75 - 10 = 65 \]

- From 65 to 315:
- Again, we multiply 65 by 5 and then subtract 10:
\[ 65 \times 5 - 10 = 325 - 10 = 315 \]

### Step 3: Apply the pattern to find the next number
Now, we can use the same operation to find the next number after 315:
\[ 315 \times 5 - 10 \]
Calculating this gives:
\[ 315 \times 5 = 1575 \]
Now subtracting 10:
\[ 1575 - 10 = 1565 \]

### Conclusion
Thus, the missing number in the series is **1565**.

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