The next number of the sequence 2,5,10,14,18,23,26,32,...... is :

Options

A. 33
B. 34
C. 36
D. 37

Answer

To find the next number in the sequence 2, 5, 10, 14, 18, 23, 26, 32, we will analyze the differences between the consecutive terms and identify a pattern.

### Step-by-Step Solution:

1. **Identify the Sequence**:
The given sequence is:
\[ 2, 5, 10, 14, 18, 23, 26, 32 \]

2. **Calculate the Differences**:
Let's calculate the differences between consecutive terms:
- \(5 - 2 = 3\)
- \(10 - 5 = 5\)
- \(14 - 10 = 4\)
- \(18 - 14 = 4\)
- \(23 - 18 = 5\)
- \(26 - 23 = 3\)
- \(32 - 26 = 6\)

So, the differences are:
\[ 3, 5, 4, 4, 5, 3, 6 \]

3. **Analyze the Differences**:
The differences do not follow a simple arithmetic pattern, so let's look at the sequence in pairs:
- The first and third terms: \(2 \to 10 \to 18 \to 26\) (increases by 8 each time)
- The second and fourth terms: \(5 \to 14 \to 23 \to 32\) (increases by 9 each time)

4. **Predict the Next Term**:
- Continuing the pattern for the first group (adding 8):
- From 26, we add 8:
\[ 26 + 8 = 34 \]
- Continuing the pattern for the second group (adding 9):
- From 32, we add 9:
\[ 32 + 9 = 41 \]

5. **Determine the Next Number**:
Since we are looking for the next number after 32 in the sequence, we will follow the first group’s pattern:
- The next number in the sequence is:
\[ 34 \]

### Conclusion:
The next number in the sequence is **34**.