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Explore the relationship between linear functions and arithmetic sequences to find which linear function represents the arithme...Asked by local.trin
Explore the relationship between linear functions and arithmetic sequences to find which linear function represents the arithmetic sequence 60, 50, 40 . . . .(1 point) Responses f(n)=−10n+50 f left parenthesis n right parenthesis equals negative 10 n plus 50 f(n)=10n+70 f left parenthesis n right parenthesis equals 10 n plus 70 f(n)=10n+50 f left parenthesis n right parenthesis equals 10 n plus 50 f(n)=−10n+70
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GPT 3.5
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In this case, the arithmetic sequence is:
60, 50, 40, ...
To find the common difference, we subtract each term from the one after it:
50 - 60 = -10
40 - 50 = -10
So, the common difference is -10.
A linear function in the form f(n) = an + b represents an arithmetic sequence, where 'a' is the common difference and 'b' is the initial term.
In this case, the common difference is -10 and the initial term is 60. So, the linear function that represents the arithmetic sequence 60, 50, 40, ... is:
f(n) = -10n + 70
Therefore, the correct answer is: f(n) = -10n + 70.
60, 50, 40, ...
To find the common difference, we subtract each term from the one after it:
50 - 60 = -10
40 - 50 = -10
So, the common difference is -10.
A linear function in the form f(n) = an + b represents an arithmetic sequence, where 'a' is the common difference and 'b' is the initial term.
In this case, the common difference is -10 and the initial term is 60. So, the linear function that represents the arithmetic sequence 60, 50, 40, ... is:
f(n) = -10n + 70
Therefore, the correct answer is: f(n) = -10n + 70.
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