Write the first three terms of the sequence defined by
(i) `a_(n)=n(n+2)` (ii) `a_(n)=n/(n+1)`

Answer

To solve the question, we will find the first three terms of the sequences defined by the given formulas.

### (i) For the sequence defined by \( a_n = n(n + 2) \):

1. **Calculate \( a_1 \)**:
\[ a_1 = 1(1 + 2) = 1 \times 3 = 3 \]

2. **Calculate \( a_2 \)**:
\[ a_2 = 2(2 + 2) = 2 \times 4 = 8 \]

3. **Calculate \( a_3 \)**:
\[ a_3 = 3(3 + 2) = 3 \times 5 = 15 \]

Thus, the first three terms of the sequence \( a_n = n(n + 2) \) are:
\[ 3, 8, 15 \]

### (ii) For the sequence defined by \( a_n = \frac{n}{n + 1} \):

1. **Calculate \( a_1 \)**:
\[ a_1 = \frac{1}{1 + 1} = \frac{1}{2} \]

2. **Calculate \( a_2 \)**:
\[ a_2 = \frac{2}{2 + 1} = \frac{2}{3} \]

3. **Calculate \( a_3 \)**:
\[ a_3 = \frac{3}{3 + 1} = \frac{3}{4} \]

Thus, the first three terms of the sequence \( a_n = \frac{n}{n + 1} \) are:
\[ \frac{1}{2}, \frac{2}{3}, \frac{3}{4} \]

### Final Answers:
- For \( a_n = n(n + 2) \): **3, 8, 15**
- For \( a_n = \frac{n}{n + 1} \): **\(\frac{1}{2}, \frac{2}{3}, \frac{3}{4}\)**

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