Write the first five terms of each of the sequences in Questions 1 to 6 whose nth terms are :
`a_(n)=(-1)^(n-1).5^(n+1)`

Explanation

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

### Step-by-step solution:

1. **Calculate \( a_1 \)**:
\[ a_1 = (-1)^{1-1} \cdot 5^{1+1} = (-1)^0 \cdot 5^2 = 1 \cdot 25 = 25 \]

2. **Calculate \( a_2 \)**:
\[ a_2 = (-1)^{2-1} \cdot 5^{2+1} = (-1)^1 \cdot 5^3 = -1 \cdot 125 = -125 \]

3. **Calculate \( a_3 \)**:
\[ a_3 = (-1)^{3-1} \cdot 5^{3+1} = (-1)^2 \cdot 5^4 = 1 \cdot 625 = 625 \]

4. **Calculate \( a_4 \)**:
\[ a_4 = (-1)^{4-1} \cdot 5^{4+1} = (-1)^3 \cdot 5^5 = -1 \cdot 3125 = -3125 \]

5. **Calculate \( a_5 \)**:
\[ a_5 = (-1)^{5-1} \cdot 5^{5+1} = (-1)^4 \cdot 5^6 = 1 \cdot 15625 = 15625 \]

### Summary of the first five terms:
- \( a_1 = 25 \)
- \( a_2 = -125 \)
- \( a_3 = 625 \)
- \( a_4 = -3125 \)
- \( a_5 = 15625 \)

Thus, the first five terms of the sequence are:
\[ 25, -125, 625, -3125, 15625 \]