If general term of a sequence is ` n(n + 1)(2n + 1), `
then its ` 5^(th)` term is

Options

A. 110
B. 155
C. 330
D. 420

Answer

To find the fifth term of the sequence given by the general term \( A_n = n(n + 1)(2n + 1) \), we will substitute \( n = 5 \) into the formula.

### Step-by-Step Solution:

1. **Identify the General Term**:
The general term of the sequence is given by:
\[ A_n = n(n + 1)(2n + 1) \]

2. **Substitute \( n = 5 \)**:
To find the fifth term, substitute \( n \) with 5:
\[ A_5 = 5(5 + 1)(2 \cdot 5 + 1) \]

3. **Calculate \( 5 + 1 \)**:
Calculate \( 5 + 1 \):
\[ 5 + 1 = 6 \]

4. **Calculate \( 2 \cdot 5 + 1 \)**:
Calculate \( 2 \cdot 5 + 1 \):
\[ 2 \cdot 5 + 1 = 10 + 1 = 11 \]

5. **Combine the Results**:
Now substitute back into the equation:
\[ A_5 = 5 \cdot 6 \cdot 11 \]

6. **Calculate \( 5 \cdot 6 \)**:
First, calculate \( 5 \cdot 6 \):
\[ 5 \cdot 6 = 30 \]

7. **Calculate \( 30 \cdot 11 \)**:
Now multiply \( 30 \) by \( 11 \):
\[ 30 \cdot 11 = 330 \]

8. **Final Result**:
Thus, the fifth term \( A_5 \) is:
\[ A_5 = 330 \]

### Final Answer:
The fifth term of the sequence is \( \boxed{330} \).