To find the first three terms of the sequence defined by [tex]\( f(n) = -2n + 7 \)[/tex], we'll follow these steps for [tex]\( n = 1, 2, \)[/tex] and [tex]\( 3 \)[/tex]:
1. Determine the first term ([tex]\( f(1) \)[/tex]):
- Substitute [tex]\( n = 1 \)[/tex] into the function:
[tex]\[
f(1) = -2(1) + 7
\][/tex]
- Perform the multiplication:
[tex]\[
f(1) = -2 \cdot 1 + 7 = -2 + 7
\][/tex]
- Add the results:
[tex]\[
f(1) = 5
\][/tex]
2. Determine the second term ([tex]\( f(2) \)[/tex]):
- Substitute [tex]\( n = 2 \)[/tex] into the function:
[tex]\[
f(2) = -2(2) + 7
\][/tex]
- Perform the multiplication:
[tex]\[
f(2) = -2 \cdot 2 + 7 = -4 + 7
\][/tex]
- Add the results:
[tex]\[
f(2) = 3
\][/tex]
3. Determine the third term ([tex]\( f(3) \)[/tex]):
- Substitute [tex]\( n = 3 \)[/tex] into the function:
[tex]\[
f(3) = -2(3) + 7
\][/tex]
- Perform the multiplication:
[tex]\[
f(3) = -2 \cdot 3 + 7 = -6 + 7
\][/tex]
- Add the results:
[tex]\[
f(3) = 1
\][/tex]
Thus, the first three terms of the sequence are:
[tex]\[
5, 3, 1
\][/tex]
