C1.4

represent a sequence algebraically using a recursion formula, function notation, or the formula for the nth term [e.g., represent 2, 4, 8, 16, 32, 64, … as $t_1=2$; $t_n=2t_{n-1}$, as $f(n)=2^n$, or as $t_n=2^n$, or represent $\frac{1}{2}$, $\frac{2}{3}$, $\frac{3}{4}$, $\frac{4}{5}$, $\frac{5}{6}$, $\frac{6}{7}$, … as $t_1=\frac{1}{2}$; $t_n=t_{n-1}+\frac{1}{n(n+1)}$, as $f(n)=\frac{n}{n+1}$, or as $t_n=\frac{n}{n+1}$, where $n$ is a natural number], and describe the information that can be obtained by inspecting each representation (e.g., function notation or the formula for the nth term may show the type of function; a recursion formula shows the relationship between terms) Sample problem: Represent the sequence 0, 3, 8, 15, 24, 35, … using a recursion formula, function notation, and the formula for the nth term. Explain why this sequence can be described as a discrete quadratic function. Explore how to identify a sequence as a discrete quadratic function by inspecting the recursion formula.