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 linear function that represents this arithmetic sequence, we first need to determine the common difference. The common difference between consecutive terms can be calculated by subtracting the previous term from the current term. In this case:
50 - 60 = -10
40 - 50 = -10
Since the common difference is -10, we know that the general form of the linear function representing this arithmetic sequence is of the form:
f(x) = mx + b
where m is the common difference and b is the y-intercept. Therefore, the linear function representing the arithmetic sequence 60, 50, 40 is:
f(x) = -10x + b
To find the y-intercept b, we can substitute any term from the sequence into the linear function. Let's substitute the first term of the sequence, 60:
f(1) = -10(1) + b
60 = -10 + b
b = 70
Therefore, the linear function representing the arithmetic sequence 60, 50, 40 is:
f(x) = -10x + 70
explore the relationship between linear functions and arithmetic sequences to find which linear function represents the arithmetic sequence 60,50,40
1 answer