Question
An arithmetic sequence follows the formula \( a_{n}=8.4+3.2 n \). The first term is [Select ] The common difference is [Select ]
Ask by Phillips Savage. in Japan
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The first term is 11.6 and the common difference is 3.2.
Solution
In the arithmetic sequence given by the formula \( a_{n} = 8.4 + 3.2n \), we can identify the first term and the common difference as follows:
1. **First Term (\( a_1 \))**:
- To find the first term, substitute \( n = 1 \) into the formula:
\[
a_1 = 8.4 + 3.2(1) = 8.4 + 3.2 = 11.6
\]
2. **Common Difference (\( d \))**:
- The coefficient of \( n \) in the formula represents the common difference. Therefore:
\[
d = 3.2
\]
**Summary**:
- **First term**: \( 11.6 \)
- **Common difference**: \( 3.2 \)
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Simplify this solution Bonus Knowledge
The first term of the arithmetic sequence occurs when \( n = 0 \). Plugging this into the formula gives us \( a_{0} = 8.4 + 3.2(0) = 8.4 \). So, the first term is \( 8.4 \). The common difference in an arithmetic sequence is the term that is added to each consecutive term to get the next one. In this case, it's the coefficient of \( n \) in the formula, which is \( 3.2 \). Thus, the common difference is \( 3.2 \).
