find the next term in the series
2, 5, 10, 17, 26, 37, 50

Options

A. 17
B. 26
C. 37
D. 65

Explanation

To find the next term in the series 2, 5, 10, 17, 26, 37, 50, we will analyze the differences between the terms step by step.

### Step 1: Identify the given series
The series is:
\[ 2, 5, 10, 17, 26, 37, 50 \]

### Step 2: Calculate the differences between consecutive terms
Let's find the differences between each pair of consecutive terms:
- \( 5 - 2 = 3 \)
- \( 10 - 5 = 5 \)
- \( 17 - 10 = 7 \)
- \( 26 - 17 = 9 \)
- \( 37 - 26 = 11 \)
- \( 50 - 37 = 13 \)

So, the differences are:
\[ 3, 5, 7, 9, 11, 13 \]

### Step 3: Identify the pattern in the differences
Now, let's look at the differences:
- The differences are increasing by 2 each time:
- \( 5 - 3 = 2 \)
- \( 7 - 5 = 2 \)
- \( 9 - 7 = 2 \)
- \( 11 - 9 = 2 \)
- \( 13 - 11 = 2 \)

### Step 4: Predict the next difference
Following the pattern, the next difference after 13 should be:
\[ 13 + 2 = 15 \]

### Step 5: Calculate the next term in the series
To find the next term in the series, we add this next difference (15) to the last term (50):
\[ 50 + 15 = 65 \]

### Conclusion
Thus, the next term in the series is:
\[ \boxed{65} \]

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