If `t_(n)=n(n+3)`, find the difference of its 5th term and 2nd term i.e., `t_(5)-t_(2)`

Answer

To solve the problem, we need to find the difference between the 5th term and the 2nd term of the sequence defined by \( t_n = n(n + 3) \).

### Step-by-Step Solution:

1. **Find the 5th term \( t_5 \)**:
\[ t_5 = 5(5 + 3) \]
- Calculate \( 5 + 3 \):
\[ 5 + 3 = 8 \]
- Now multiply:
\[ t_5 = 5 \times 8 = 40 \]

2. **Find the 2nd term \( t_2 \)**:
\[ t_2 = 2(2 + 3) \]
- Calculate \( 2 + 3 \):
\[ 2 + 3 = 5 \]
- Now multiply:
\[ t_2 = 2 \times 5 = 10 \]

3. **Calculate the difference \( t_5 - t_2 \)**:
\[ t_5 - t_2 = 40 - 10 \]
- Perform the subtraction:
\[ 40 - 10 = 30 \]

### Final Answer:
The difference between the 5th term and the 2nd term is \( 30 \).

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