Question
Write the first five terms of the sequence. \( f(0)=-7, f(n)=f(n-1)+8 \)
Ask by Barrett Vaughan. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The first five terms of the sequence are -7, 1, 9, 17, and 25.
Solution
To find the first five terms of the sequence defined by \( f(0) = -7 \) and \( f(n) = f(n-1) + 8 \), we will calculate each term step by step.
1. **First term**:
\[
f(0) = -7
\]
2. **Second term**:
\[
f(1) = f(0) + 8 = -7 + 8 = 1
\]
3. **Third term**:
\[
f(2) = f(1) + 8 = 1 + 8 = 9
\]
4. **Fourth term**:
\[
f(3) = f(2) + 8 = 9 + 8 = 17
\]
5. **Fifth term**:
\[
f(4) = f(3) + 8 = 17 + 8 = 25
\]
Now, we can summarize the first five terms of the sequence:
- \( f(0) = -7 \)
- \( f(1) = 1 \)
- \( f(2) = 9 \)
- \( f(3) = 17 \)
- \( f(4) = 25 \)
Thus, the first five terms of the sequence are:
\[
-7, 1, 9, 17, 25
\]
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Simplify this solution Extra Insights
The first term of the sequence starts with \( f(0) = -7 \). To find the subsequent terms, we use the recursive formula \( f(n) = f(n-1) + 8 \). So, the next terms are: - \( f(1) = f(0) + 8 = -7 + 8 = 1 \) - \( f(2) = f(1) + 8 = 1 + 8 = 9 \) - \( f(3) = f(2) + 8 = 9 + 8 = 17 \) - \( f(4) = f(3) + 8 = 17 + 8 = 25 \) Thus, the first five terms of the sequence are: -7, 1, 9, 17, 25.
