Question

Explore the relationship between linear functions and arithmetic sequences to find which linear function represents the arithmetic sequence 60, 50, 40 . . . .(1 point)

Answer 1

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In the case of the sequence 60, 50, 40, the common difference is -10.

To find the linear function that represents this arithmetic sequence, we can use the formula for an arithmetic sequence:

an = a1 + (n-1)d

where:
- an is the nth term of the sequence
- a1 is the first term of the sequence
- d is the common difference between terms
- n is the position of the term in the sequence

In this case, a1 = 60, d = -10, and we want to find the nth term of the sequence. Let's substitute these values into the formula:

a_n = 60 + (n-1)(-10)
a_n = 60 - 10n + 10
a_n = 70 - 10n

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