Question

A table of values of a linear function is shown below. Find the output when the input is n. Type your answer in the space provided. Input numbers: 1, 2, 3, 4, n. Output numbers: 3, 1, -1, -3, _. Can someone please quickly explain this to me?

Answer 1

Answer:

  5 -2n

Step-by-step explanation:

There are several ways you can find the linear function for this table of values.

• find the slope and intercept and write the slope-intercept equation
• find the slope and use a point to write the point-slope equation; solve for y
• recognize the x-values are sequential starting with 1, so the y-values are an arithmetic sequence; write the formula for the n-th term of an arithmetic sequence

Using the last approach, we see that the first term is 3, and the common difference is 1-3 = -2. Then the n-th term is ...

  an = a1 +d(n-1) . . . . . . general term of arithmetic sequence with first term a1 and common difference d

  an = 3 -2(n-1) . . . . sequence with a1=3, d=-2

The output when the input is n is ...

  3 -2(n -1)

This can be simplified to ...

  5 -2n . . . . output for input of n