The 44th terms of the following sequence `1,2,3,10,11,12,13,20,21,22,23,30,31,….` is :

Options

A. 1331
B. 17776
C. 12330
D. 13330

Answer

To find the 44th term of the sequence `1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, ...`, we can analyze the pattern of the sequence step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The sequence consists of numbers that can be grouped based on their tens place. The numbers are:
- From 1 to 3: `1, 2, 3`
- From 10 to 13: `10, 11, 12, 13`
- From 20 to 23: `20, 21, 22, 23`
- From 30 to 33: `30, 31, 32, 33`
- And so on...

2. **Count the Terms**:
- The first group (1 to 3) has 3 terms.
- The second group (10 to 13) has 4 terms.
- The third group (20 to 23) has 4 terms.
- The fourth group (30 to 33) has 4 terms.
- Continuing this pattern, we can see that every group starting from 10 contributes 4 terms.

3. **Calculate the Total Terms**:
- The first group contributes 3 terms.
- The next groups (10s, 20s, 30s, etc.) contribute 4 terms each.
- To find out how many complete groups we have until we reach the 44th term, we can calculate:
- 3 (from the first group) + 4n (from the subsequent groups) = 44
- 4n = 44 - 3
- 4n = 41
- n = 41 / 4 = 10.25

This means we have 10 complete groups of 4 terms from the 10s onwards.

4. **Determine the Group of the 44th Term**:
- The first group contributes 3 terms.
- The next 10 groups contribute 40 terms (10 groups × 4 terms each).
- Therefore, the 43rd term is the last term of the 10th group (which is 30 to 33).
- The 44th term will be the first term of the next group, which is the 11th group (40 to 43).

5. **Find the 44th Term**:
- The first term of the 11th group (40s) is `40`.

Thus, the 44th term of the sequence is **40**.