To find the next 4 terms of the sequence given [tex]\( a = 3 \)[/tex] and the recursive formula [tex]\( a_n = a_{n-1} - 2 \)[/tex], follow these steps:
### Step 1: Identify the first term
The first term of the sequence is given as:
[tex]\[ a_1 = 3 \][/tex]
### Step 2: Use the recursive formula to find the next terms
Using the formula [tex]\( a_n = a_{n-1} - 2 \)[/tex], we can generate the next terms:
- Second term:
[tex]\[ a_2 = a_1 - 2 \][/tex]
Substituting [tex]\( a_1 = 3 \)[/tex]:
[tex]\[ a_2 = 3 - 2 = 1 \][/tex]
- Third term:
[tex]\[ a_3 = a_2 - 2 \][/tex]
Substituting [tex]\( a_2 = 1 \)[/tex]:
[tex]\[ a_3 = 1 - 2 = -1 \][/tex]
- Fourth term:
[tex]\[ a_4 = a_3 - 2 \][/tex]
Substituting [tex]\( a_3 = -1 \)[/tex]:
[tex]\[ a_4 = -1 - 2 = -3 \][/tex]
- Fifth term:
[tex]\[ a_5 = a_4 - 2 \][/tex]
Substituting [tex]\( a_4 = -3 \)[/tex]:
[tex]\[ a_5 = -3 - 2 = -5 \][/tex]
### Step 3: List all the terms
Including the initial term and the next four terms we calculated, the sequence is:
[tex]\[ 3, 1, -1, -3, -5 \][/tex]
Thus, the next 4 terms of the sequence are:
[tex]\[ 1, -1, -3, -5 \][/tex]
