Write first five terms of a sequence where `n^(th)` term is defined by `a_(n)=n^(2)+n`.

Answer

To find the first five terms of the sequence defined by the nth term \( a_n = n^2 + n \), we will substitute values of \( n \) from 1 to 5 into the formula.

### Step-by-Step Solution:

1. **Find the first term \( a_1 \)**:
\[ a_1 = 1^2 + 1 = 1 + 1 = 2 \]

2. **Find the second term \( a_2 \)**:
\[ a_2 = 2^2 + 2 = 4 + 2 = 6 \]

3. **Find the third term \( a_3 \)**:
\[ a_3 = 3^2 + 3 = 9 + 3 = 12 \]

4. **Find the fourth term \( a_4 \)**:
\[ a_4 = 4^2 + 4 = 16 + 4 = 20 \]

5. **Find the fifth term \( a_5 \)**:
\[ a_5 = 5^2 + 5 = 25 + 5 = 30 \]

### Summary of the First Five Terms:
- \( a_1 = 2 \)
- \( a_2 = 6 \)
- \( a_3 = 12 \)
- \( a_4 = 20 \)
- \( a_5 = 30 \)

Thus, the first five terms of the sequence are **2, 6, 12, 20, 30**.