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