Explore the relationship between linear functions and arithmetic sequences to find which linear function represents the arithmetic sequence 60, 50, 40....
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. In other words, if the sequence is denoted by {a_n}, the difference between a_(n+1) and a_n is always the same.
For the arithmetic sequence 60, 50, 40..., we can see that the common difference between each term is -10. This is because 60 - 50 = 10, 50 - 40 = 10, and so on.
Now let's consider a linear function in the form of y = mx + b, where m is the slope and b is the y-intercept.
Since the common difference of the arithmetic sequence is -10, the slope of the linear function representing this sequence will also be -10. This is because the slope of a linear function represents the rate of change between each term.
To find the y-intercept, we can substitute one of the terms from the sequence into the linear function. Let's use the first term, 60:
60 = -10(1) + b
60 = -10 + b
b = 70
Therefore, the linear function representing the arithmetic sequence 60, 50, 40... is y = -10x + 70.