Task Sets: Recognize sequences as functions - Common Core Math - HS Functions

1.

The arithmetic sequence has first term $a(1) = 7$ and common difference $d = -3$ .

Use the explicit formula $a(n) = a_1 + d(n - 1)$ to find $a(6)$ .

2.

A student defines a sequence with only the rule $a(n) = a(n-1) + 5$ .
Why is this definition incomplete?

A.

The recurrence relation should subtract, not add.

B.

An initial term such as $a(1) = \text{some value}$ is missing; without it,
the sequence is not uniquely determined.

C.

The notation $a(n)$ should be replaced with $a_n$ .

D.

The rule must also state the common ratio.

3.

The sequence 3, 7, 11, 15, … has explicit formula $a(n) = 4n - 1$ and
recursive definition $a(1) = 3$ , $a(n) = a(n-1) + 4$ for $n \geq 2$ .

Use the recursive definition to compute $a(4)$ .

4.

The geometric sequence has first term $a(1) = 4$ and common ratio $r = 3$ .

Use the explicit formula $a(n) = a_1 \cdot r^{n-1}$ to find $a(4)$ .

5.

The Fibonacci sequence is defined by $f(0) = 1$ , $f(1) = 1$ , and
$f(n+1) = f(n) + f(n-1)$ for $n \geq 1$ .

What is $f(5)$ ?

HSF.IF.A.3 Tutor Intake — Sequences as Functions