An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The general form for an arithmetic sequence is:
a_n = a_1 + (n - 1)d
where a_n is the nth term in the sequence, a_1 is the first term, n is the term number, and d is the common difference between terms.
In the given sequence 60, 50, 40, the first term is a_1 = 60 and the common difference is d = -10, since each term decreases by 10.
Now, we can find the linear function that represents this arithmetic sequence. We know that the general form of a linear function is:
f(x) = mx + b
where m is the slope and b is the y-intercept.
Since the common difference is -10, the slope of the linear function representing the arithmetic sequence will be -10. We can choose any term from the sequence and the corresponding position to find the y-intercept. Let's choose the second term (50, position 2).
Using the formula for the nth term of an arithmetic sequence, we can find the y-intercept:
50 = 60 + (2-1)(-10)
50 = 60 - 10
50 = 50
Therefore, the y-intercept is 50.
Putting it all together, the linear function representing the arithmetic sequence 60, 50, 40 is:
f(x) = -10x + 50
Explore the relationship between linear functions and arithmetic sequences to find which linear function represents the arithmetic sequence 60, 50, 40 . . . .
1 answer
1 answer