nth term of the sequence:
`5,2,-1,-4,-7,` is…………

Answer

To find the nth term of the sequence \(5, 2, -1, -4, -7\), we can observe the pattern in the sequence.

### Step-by-step Solution:

1. **Identify the Sequence**:
The given sequence is \(5, 2, -1, -4, -7\).

2. **Find the Common Difference**:
To find the common difference \(d\), we subtract each term from the next:
- \(2 - 5 = -3\)
- \(-1 - 2 = -3\)
- \(-4 - (-1) = -3\)
- \(-7 - (-4) = -3\)

Thus, the common difference \(d = -3\).

3. **Identify the First Term**:
The first term \(a\) of the sequence is \(5\).

4. **Use the Formula for the nth Term of an Arithmetic Sequence**:
The formula for the nth term \(T_n\) of an arithmetic sequence is given by:
\[ T_n = a + (n - 1)d \]
Substituting the values of \(a\) and \(d\):
\[ T_n = 5 + (n - 1)(-3) \]

5. **Simplify the Expression**:
\[ T_n = 5 - 3(n - 1) \]
\[ T_n = 5 - 3n + 3 \]
\[ T_n = 8 - 3n \]

### Final Answer:
Thus, the nth term of the sequence is:
\[ T_n = 8 - 3n \]