Find the next number in the given series.
8, 14, 23, ?, 50

Options

A. 35
B. 34
C. 38
D. 40

Answer

To find the next number in the series 8, 14, 23, ?, 50, we can follow these steps:

### Step 1: Identify the differences between consecutive numbers
First, we will calculate the differences between the numbers in the series:
- Difference between 14 and 8:
\( 14 - 8 = 6 \)
- Difference between 23 and 14:
\( 23 - 14 = 9 \)
- Difference between 50 and 23:
\( 50 - 23 = 27 \)

So, we have the differences: 6, 9, ?, 27.

### Step 2: Analyze the pattern in the differences
Next, we can observe the differences we calculated:
- The first difference is 6.
- The second difference is 9.

Now, let's find the difference between these two differences:
- Difference between 9 and 6:
\( 9 - 6 = 3 \)

### Step 3: Predict the next difference
If we continue this pattern, we can assume that the next difference will increase by 3 again:
- Next difference:
\( 9 + 3 = 12 \)

### Step 4: Calculate the missing number
Now we can find the missing number in the series by adding this difference to the last known number (23):
- Missing number:
\( 23 + 12 = 35 \)

### Step 5: Verify with the next number in the series
To ensure our answer is correct, we can check the next number:
- The difference between 35 and 23 is 12.
- The difference between 50 and 35 is:
\( 50 - 35 = 15 \)

Now, we can see that the differences are 6, 9, 12, and 15, which indeed follows the pattern of increasing by 3.

Thus, the next number in the series is **35**.