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
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