Write the first five terms of the following sequence amd obtain the corresponding series.
`a_(1)=a_(2)=2,a_(n)=a_(n-1)-1,ngt2`

Explanation

To solve the problem, we need to find the first five terms of the sequence defined by the recurrence relation and then obtain the corresponding series.

### Step 1: Identify the initial conditions and the recurrence relation
We are given:
- \( a_1 = 2 \)
- \( a_2 = 2 \)
- For \( n > 2 \), \( a_n = a_{n-1} - 1 \)

### Step 2: Calculate the terms of the sequence
Now, we will calculate the terms of the sequence one by one.

1. **Calculate \( a_3 \)**:
\[ a_3 = a_2 - 1 = 2 - 1 = 1 \]

2. **Calculate \( a_4 \)**:
\[ a_4 = a_3 - 1 = 1 - 1 = 0 \]

3. **Calculate \( a_5 \)**:
\[ a_5 = a_4 - 1 = 0 - 1 = -1 \]

### Step 3: Write the first five terms of the sequence
The first five terms of the sequence are:
\[ a_1 = 2, \quad a_2 = 2, \quad a_3 = 1, \quad a_4 = 0, \quad a_5 = -1 \]

### Step 4: Write the corresponding series
The corresponding series is obtained by adding the terms:
\[ S = a_1 + a_2 + a_3 + a_4 + a_5 = 2 + 2 + 1 + 0 - 1 \]

### Step 5: Summarize the results
Thus, the first five terms of the sequence are:
\[ 2, 2, 1, 0, -1 \]
And the corresponding series is:
\[ 2 + 2 + 1 + 0 - 1 \]