Find `a_(3),a_(5),a_(8)` if the `n^(th)` term is given by `a_(n)=(-1)^(n)n`

Answer

To find the values of \( a_3 \), \( a_5 \), and \( a_8 \) given the \( n^{th} \) term formula \( a_n = (-1)^n n \), we will substitute the respective values of \( n \) into the formula.

### Step 1: Calculate \( a_3 \)
Using the formula:
\[ a_3 = (-1)^3 \cdot 3 \]
Calculating \( (-1)^3 \):
\[ (-1)^3 = -1 \]
Now substituting back:
\[ a_3 = -1 \cdot 3 = -3 \]

### Step 2: Calculate \( a_5 \)
Using the formula:
\[ a_5 = (-1)^5 \cdot 5 \]
Calculating \( (-1)^5 \):
\[ (-1)^5 = -1 \]
Now substituting back:
\[ a_5 = -1 \cdot 5 = -5 \]

### Step 3: Calculate \( a_8 \)
Using the formula:
\[ a_8 = (-1)^8 \cdot 8 \]
Calculating \( (-1)^8 \):
\[ (-1)^8 = 1 \]
Now substituting back:
\[ a_8 = 1 \cdot 8 = 8 \]

### Final Answers
Thus, the values are:
- \( a_3 = -3 \)
- \( a_5 = -5 \)
- \( a_8 = 8 \)