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+70 f left parenthesis n right parenthesis equals 10 n plus 70 f(n)=10n+50

1 answer

To find the linear function that represents the arithmetic sequence 60, 50, 40 ..., we can look for the common difference between the terms.

In this case, the common difference is -10, as each term decreases by 10.

The general form of an arithmetic sequence is given by the formula:
a_n = a_1 + (n-1)d

Where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference.

In this sequence, the first term a_1 is 60, and the common difference d is -10.

Substitute these values into the formula to find the linear function that represents the arithmetic sequence:
a_n = 60 + (n-1)(-10)
a_n = 60 - 10n + 10
a_n = -10n + 70

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

The correct answer is:
f(n) = -10n + 70