5 15 35 75 155 (?)

Options

A. 295
B. 315
C. 275
D. 305

Explanation

To solve the series: 5, 15, 35, 75, 155, (?), we will follow these steps:

### Step 1: Identify the given series
The series provided is: 5, 15, 35, 75, 155.

### Step 2: Calculate the differences between consecutive terms
We will find the difference between each pair of consecutive terms:

- Difference between 15 and 5:
\( 15 - 5 = 10 \)

- Difference between 35 and 15:
\( 35 - 15 = 20 \)

- Difference between 75 and 35:
\( 75 - 35 = 40 \)

- Difference between 155 and 75:
\( 155 - 75 = 80 \)

Now we have the differences:
- 10, 20, 40, 80.

### Step 3: Analyze the pattern in the differences
The differences we calculated are:
- 10, 20, 40, 80.

We can observe that each difference is doubling the previous one:
- \( 10 \times 2 = 20 \)
- \( 20 \times 2 = 40 \)
- \( 40 \times 2 = 80 \)

Following this pattern, the next difference should be:
- \( 80 \times 2 = 160 \)

### Step 4: Calculate the next term in the series
To find the next term in the original series, we will add the next difference (160) to the last term (155):
- \( 155 + 160 = 315 \)

### Conclusion
Thus, the next number in the series is **315**.

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