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 5th term of the sequence given by the general term \( T_n = n(n + 1)(2n + 1) \), 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 as:
\[ T_n = n(n + 1)(2n + 1) \]

2. **Substitute \( n = 5 \)**: To find the 5th term, we substitute \( n = 5 \) into the general term:
\[ T_5 = 5(5 + 1)(2 \cdot 5 + 1) \]

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

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

5. **Substitute the values back into the equation**: Now we have:
\[ T_5 = 5 \cdot 6 \cdot 11 \]

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

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

8. **Final result**: Therefore, the 5th term of the sequence is:
\[ T_5 = 330 \]