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+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

Answer 1

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.