To find the first three terms of the sequence defined by the function [tex]\( f(n) = -2n + 3 \)[/tex], we start by evaluating the function for the first three values of [tex]\( n \)[/tex].
### Step 1: Calculate the First Term ([tex]\( n = 1 \)[/tex])
For [tex]\( n = 1 \)[/tex]:
[tex]\[
f(1) = -2(1) + 3
\][/tex]
Perform the multiplication:
[tex]\[
-2 \cdot 1 = -2
\][/tex]
Then add 3 to -2:
[tex]\[
f(1) = -2 + 3 = 1
\][/tex]
So, the first term is [tex]\( 1 \)[/tex].
### Step 2: Calculate the Second Term ([tex]\( n = 2 \)[/tex])
For [tex]\( n = 2 \)[/tex]:
[tex]\[
f(2) = -2(2) + 3
\][/tex]
Perform the multiplication:
[tex]\[
-2 \cdot 2 = -4
\][/tex]
Then add 3 to -4:
[tex]\[
f(2) = -4 + 3 = -1
\][/tex]
So, the second term is [tex]\( -1 \)[/tex].
### Step 3: Calculate the Third Term ([tex]\( n = 3 \)[/tex])
For [tex]\( n = 3 \)[/tex]:
[tex]\[
f(3) = -2(3) + 3
\][/tex]
Perform the multiplication:
[tex]\[
-2 \cdot 3 = -6
\][/tex]
Then add 3 to -6:
[tex]\[
f(3) = -6 + 3 = -3
\][/tex]
So, the third term is [tex]\( -3 \)[/tex].
### Final Answer
The first three terms of the sequence are:
[tex]\[
1, -1, -3
\][/tex]
Thus, the first three terms of the sequence defined by [tex]\( f(n) = -2n + 3 \)[/tex] are [tex]\( 1 \)[/tex], [tex]\( -1 \)[/tex], and [tex]\( -3 \)[/tex].
