To determine which of Ivy and Andrey provided the correct formula for the sequence [tex]\(-100, -50, 0, 50, \ldots\)[/tex], we will verify both of their formulas step-by-step.
### Step-by-Step Solution:
1. Examine Ivy's Formula: [tex]\( f(n) = -100 + 50(n - 1) \)[/tex]
Let's calculate the first few terms using Ivy's formula:
- For [tex]\( n = 1 \)[/tex]:
[tex]\[
f(1) = -100 + 50(1 - 1) = -100 + 0 = -100
\][/tex]
- For [tex]\( n = 2 \)[/tex]:
[tex]\[
f(2) = -100 + 50(2 - 1) = -100 + 50 = -50
\][/tex]
- For [tex]\( n = 3 \)[/tex]:
[tex]\[
f(3) = -100 + 50(3 - 1) = -100 + 100 = 0
\][/tex]
- For [tex]\( n = 4 \)[/tex]:
[tex]\[
f(4) = -100 + 50(4 - 1) = -100 + 150 = 50
\][/tex]
Ivy's formula matches the given sequence [tex]\(-100, -50, 0, 50\)[/tex].
2. Examine Andrey's Formula: [tex]\( f(n) = -150 + 50n \)[/tex]
Now, let's calculate the first few terms using Andrey's formula:
- For [tex]\( n = 1 \)[/tex]:
[tex]\[
f(1) = -150 + 50(1) = -150 + 50 = -100
\][/tex]
- For [tex]\( n = 2 \)[/tex]:
[tex]\[
f(2) = -150 + 50(2) = -150 + 100 = -50
\][/tex]
- For [tex]\( n = 3 \)[/tex]:
[tex]\[
f(3) = -150 + 50(3) = -150 + 150 = 0
\][/tex]
- For [tex]\( n = 4 \)[/tex]:
[tex]\[
f(4) = -150 + 50(4) = -150 + 200 = 50
\][/tex]
Andrey's formula also matches the given sequence [tex]\(-100, -50, 0, 50\)[/tex].
Since both formulas, [tex]\( f(n) = -100 + 50(n - 1) \)[/tex] by Ivy and [tex]\( f(n) = -150 + 50n \)[/tex] by Andrey, correctly produce the given sequence, the right answer is:
(C) Both Ivy and Andrey
