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 where the first term is 1 and each subsequent term is obtained by adding \( n+1 \) to the \( n \)th term, we can follow these steps:

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

2. **Calculate the second term**: The second term \( a_2 \) can be calculated using the formula:
\[ a_2 = a_1 + (1 + 1) = 1 + 2 = 3 \]

3. **Calculate the third term**: The third term \( a_3 \) is calculated as:
\[ a_3 = a_2 + (2 + 1) = 3 + 3 = 6 \]

4. **Calculate the fourth term**: The fourth term \( a_4 \) is calculated as:
\[ a_4 = a_3 + (3 + 1) = 6 + 4 = 10 \]

5. **Calculate the fifth term**: The fifth term \( a_5 \) is calculated as:
\[ a_5 = a_4 + (4 + 1) = 10 + 5 = 15 \]

6. **Calculate the sixth term**: Finally, the sixth term \( a_6 \) is calculated as:
\[ a_6 = a_5 + (5 + 1) = 15 + 6 = 21 \]

Thus, the 6th term of the sequence is:
\[ \boxed{21} \]