2,5,10,17,26,37,50,64

Options

A. 50
B. 26
C. 37
D. 64

Answer

To find the next term in the series: 2, 5, 10, 17, 26, 37, 50, 64, we will analyze the pattern in the sequence step by step.

### Step 1: Identify the given series
The series provided is:
2, 5, 10, 17, 26, 37, 50, 64

### Step 2: Calculate the differences between consecutive terms
Let's calculate 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
- 64 - 50 = 14

So, the differences are:
3, 5, 7, 9, 11, 13, 14

### Step 3: Analyze the differences
Now, let's look at the pattern in the differences:
- The first differences are: 3, 5, 7, 9, 11, 13, 14

Notice that the first five differences (3, 5, 7, 9, 11, 13) are increasing by 2 each time. However, the last difference (14) does not follow this pattern.

### Step 4: Identify the pattern in the differences
The differences can be represented as:
- 3 (which is 2 + 1)
- 5 (which is 3 + 2)
- 7 (which is 5 + 2)
- 9 (which is 7 + 2)
- 11 (which is 9 + 2)
- 13 (which is 11 + 2)
- 14 (which is an anomaly)

### Step 5: Predict the next difference
Following the established pattern, the next difference after 14 should ideally be:
- 14 + 2 = 16

### Step 6: Calculate the next term in the series
Now, we add this predicted difference to the last term in the series:
- 64 + 16 = 80

### Conclusion
Thus, the next term in the series is **80**.