Question

Activity 3:

Consider the sequence that follows a "plus 3" pattern: 4, 7, 10, 13, 16...
2. Write a formula for the sequence using g(n) notation.

b. Does the formula f(n) = 3(n − 1) + 4 generate the same sequence? Why might some people prefer this
formula?

c. Graph the terms of the sequence as ordered pairs (n, f(n)) on the coordinate plane. What do you notice
about the graph?

Answer 1

b. Yes, the formula f(n) = 3(n - 1) + 4 generates the same sequence. Some people might prefer this formula because it is simpler and easier to remember than the g(n) formula.

c. When we graph the terms of the sequence as ordered pairs (n, f(n)) on the coordinate plane, we notice that the graph is a straight line with a slope of 3 and a y-intercept of 4. This makes sense because the sequence follows a "plus 3" pattern, and each term is 3 more than the previous term.