Question

3. Given the explicit formula: an = 8 + 7(n-1)

What is the common difference? _______
What is the first term? _______
Which term is the formula finding if they ask for a5? _______
What value should replace n? _______
A) 7
B) 8
C) 5th
D) 5

Answer 1

To analyze the explicit formula \( a_n = 8 + 7(n-1) \), let’s answer each of your questions step by step.

1. **What is the common difference?**
The common difference in an arithmetic sequence can be identified by looking at the coefficient of \( n \) in the formula. In this case, the formula can be expressed as \( a_n = 8 + 7n - 7 = 7n + 1 \), which shows that each term increases by 7.
**Common difference = 7**

2. **What is the first term?**
The first term can be found by substituting \( n = 1 \) into the formula:
\[
a_1 = 8 + 7(1-1) = 8 + 7(0) = 8
\]
**First term = 8**

3. **Which term is the formula finding if they ask for a5?**
The notation \( a_5 \) refers specifically to the 5th term in the sequence.
**Term = 5th**

4. **What value should replace n?**
To find \( a_5 \), we replace \( n \) with 5 in the formula. Hence, the correct option from the choices provided (7, 8, 5th, D) is:
**Value that should replace n = 5** (Answer: D)

To summarize:
- Common difference: **7**
- First term: **8**
- The term being found for \( a_5 \): **5th**
- Value to replace \( n \): **5** (D)