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+70 f left parenthesis n right parenthesis equals 10 n plus 70 f(n)=−10n+70 f left parenthesis n right parenthesis
To determine which linear function represents the arithmetic sequence 60, 50, 40..., we first need to identify the common difference between consecutive terms in the sequence.
The common difference is obtained by subtracting any two consecutive terms. In this case, if we subtract 50 from 60, we get 10, and if we subtract 40 from 50, we also get 10. This indicates that the common difference is -10.
Now we know that the linear function representing an arithmetic sequence can be written in the form f(n) = an + b, where a is the common difference and b is the initial term of the sequence.
Since the common difference is -10, the linear function would be of the form f(n) = -10n + b. To find the initial term, we can substitute the values of n = 1 and f(n) = 60 into the equation.
60 = -10(1) + b
60 = -10 + b
b = 60 + 10
b = 70
Therefore, the linear function representing the arithmetic sequence 60, 50, 40... is f(n) = -10n + 70.