13.76 14.91 17.21 20.66 ? 31.01

Options

A. 25.66
B. 24.36
C. 24.26
D. 25.26

Explanation

To solve the series: 13.76, 14.91, 17.21, 20.66, ?, 31.01, we will follow these steps:

### Step 1: Identify the given series
We have the series:
- 13.76
- 14.91
- 17.21
- 20.66
- ?
- 31.01

### Step 2: Calculate the differences between consecutive terms
Let's find the difference between each pair of consecutive terms:
1. Difference between 14.91 and 13.76:
\[ 14.91 - 13.76 = 1.15 \]
2. Difference between 17.21 and 14.91:
\[ 17.21 - 14.91 = 2.30 \]
3. Difference between 20.66 and 17.21:
\[ 20.66 - 17.21 = 3.45 \]

Now we have the differences:
- 1.15
- 2.30
- 3.45

### Step 3: Identify the pattern in the differences
The differences are:
- 1.15 (which is \(1.15 \times 1\))
- 2.30 (which is \(1.15 \times 2\))
- 3.45 (which is \(1.15 \times 3\))

This suggests that the next difference should be:
\[ 1.15 \times 4 = 4.60 \]

### Step 4: Calculate the next term in the series
To find the next term, we add the next difference (4.60) to the last known term (20.66):
\[ 20.66 + 4.60 = 25.26 \]

### Step 5: Verify the next term with the following term in the series
Now we need to check if the difference between this new term (25.26) and the next term (31.01) follows the pattern:
- Calculate the difference:
\[ 31.01 - 25.26 = 5.75 \]
- This difference should be:
\[ 1.15 \times 5 = 5.75 \]

### Conclusion
The missing term in the series is:
\[ \boxed{25.26} \]