Question

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 negative 10 n plus 70

f(n)=−10n+50
f left parenthesis n right parenthesis equals negative 10 n plus 50

f(n)=10n+50
f left parenthesis n right parenthesis equals 10 n plus 50

f(n)=10n+70

Answer 1

To find which linear function represents the arithmetic sequence 60, 50, 40, we can first determine the common difference between each term in the sequence.

From 60 to 50 is a difference of -10, and from 50 to 40 is also a difference of -10. This means that the common difference between each term in the sequence is -10.

The linear function that represents this arithmetic sequence will have a slope of -10, as this represents the common difference in the sequence. The general form of a linear function is f(n) = mx + b, where m is the slope and b is the y-intercept.

Given the common difference of -10, we can see that the linear function f(n) = -10n + b could represent the arithmetic sequence. To find the specific linear function for the sequence 60, 50, 40, we can use one of the terms in the sequence and plug it into the function:

When n = 1, f(1) = -10(1) + b = 60
-10 + b = 60
b = 70

Therefore, the linear function that represents the arithmetic sequence 60, 50, 40 is f(n) = -10n + 70.