The 444th term of the following sequences 1, 2, 3, 10, 11, 12 ,13,20, 21, 22, 23, 30, 31, … is:

Options

A. 1110
B. 17776
C. 12330
D. 13330

Answer

To find the 444th term of the sequence: 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, ..., we can analyze the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The sequence consists of numbers that can be grouped based on their tens place. The sequence starts with single digits (1, 2, 3) and then moves to numbers in the tens (10, 11, 12, 13), followed by the next set of tens (20, 21, 22, 23), and so on.

2. **Break Down the Sequence**:
- The first three terms are: 1, 2, 3 (3 terms)
- The next group is: 10, 11, 12, 13 (4 terms)
- The next group is: 20, 21, 22, 23 (4 terms)
- The next group is: 30, 31, 32, 33 (4 terms)
- This pattern continues with each group of tens contributing 4 terms after the initial three single-digit terms.

3. **Calculate the Number of Terms**:
- The first three terms contribute 3 terms.
- Each subsequent group of tens contributes 4 terms.
- To find out how many complete groups of tens fit into the remaining terms after the first three, we can calculate:
\[ \text{Remaining terms} = 444 - 3 = 441 \]
- Each group contributes 4 terms, so we calculate how many complete groups fit into 441:
\[ \text{Number of complete groups} = \frac{441}{4} = 110.25 \]
- This means there are 110 complete groups of tens, contributing \(110 \times 4 = 440\) terms.

4. **Determine the 444th Term**:
- The 440th term corresponds to the end of the 110th group, which is 10 times 110:
\[ 10 \times 110 = 1100 \]
- The 441st term is 1101, the 442nd term is 1102, the 443rd term is 1103, and the 444th term is:
\[ 1104 \]

### Final Answer:
The 444th term of the sequence is **1104**.