First term of a sequence is 1 and the `(n+1)th` term is obtained by adding `(n+1)` to the nth term for all natural numbers n, the 6th term of the sequence is

Options

A. 7
B. 13
C. 21
D. 27

Answer

To find the 6th term of the sequence defined by the given conditions, we can follow these steps:

1. **Identify the first term**: The first term of the sequence is given as \( a_1 = 1 \).

2. **Define the recursive formula**: The formula for the sequence is given as:
\[ a_{n+1} = a_n + (n + 1) \]
This means that each term is obtained by adding \( n + 1 \) to the previous term.

3. **Calculate the subsequent terms**:
- For \( n = 1 \):
\[ a_2 = a_1 + (1 + 1) = 1 + 2 = 3 \]
- For \( n = 2 \):
\[ a_3 = a_2 + (2 + 1) = 3 + 3 = 6 \]
- For \( n = 3 \):
\[ a_4 = a_3 + (3 + 1) = 6 + 4 = 10 \]
- For \( n = 4 \):
\[ a_5 = a_4 + (4 + 1) = 10 + 5 = 15 \]
- For \( n = 5 \):
\[ a_6 = a_5 + (5 + 1) = 15 + 6 = 21 \]

4. **Conclusion**: The 6th term of the sequence is:
\[ a_6 = 21 \]