To determine the first five terms of the sequence defined by the given function, let's follow the steps one-by-one:
1. Start with the first term:
[tex]\[
f(1) = -5.25
\][/tex]
So, the first term is [tex]\(-5.25\)[/tex].
2. To find the second term, use the given recursive formula [tex]\( f(n) = f(n-1) + 1.75 \)[/tex]:
[tex]\[
f(2) = f(1) + 1.75 = -5.25 + 1.75 = -3.5
\][/tex]
So, the second term is [tex]\(-3.5\)[/tex].
3. To find the third term:
[tex]\[
f(3) = f(2) + 1.75 = -3.5 + 1.75 = -1.75
\][/tex]
So, the third term is [tex]\(-1.75\)[/tex].
4. To find the fourth term:
[tex]\[
f(4) = f(3) + 1.75 = -1.75 + 1.75 = 0.0
\][/tex]
So, the fourth term is [tex]\(0.0\)[/tex].
5. To find the fifth term:
[tex]\[
f(5) = f(4) + 1.75 = 0.0 + 1.75 = 1.75
\][/tex]
So, the fifth term is [tex]\(1.75\)[/tex].
Therefore, the first five terms of the sequence are:
[tex]\[
-5.25, -3.5, -1.75, 0.0, 1.75
\][/tex]
