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

1.

The sequence $a(n) = 3n - 1$ has domain $\{1, 2, 3, 4, 5, ...\}$ . Find $a(6)$ .

2.

The sequence 4, 7, 10, 13, 16, ... is what type?

A.

Geometric, because consecutive terms have a constant ratio.

B.

Arithmetic, because consecutive terms have a constant difference of 3.

C.

Neither arithmetic nor geometric.

D.

Geometric, because the terms are always increasing.

3.

The arithmetic sequence has first term $a(1) = 5$ and common difference $d = 4$ . Use the explicit formula $a(n) = a_1 + d(n-1)$ to find $a(10)$ .

4.

The geometric sequence has first term $a(1) = 2$ and common ratio $r = 3$ . Use the explicit formula $a(n) = a_1 \cdot r^{n-1}$ to find $a(4)$ .

5.

Which of the following is a complete recursive definition for the sequence 2, 5, 8, 11, ...?

A.

$a(n) = a(n-1) + 3$ for $n \geq 2$ .

B.

$a(1) = 2; \; a(n) = a(n-1) + 3$ for $n \geq 2$ .

C.

$a(n) = 3n - 1$ .

D.

$a(1) = 2; \; a(n) = 3a(n-1)$ for $n \geq 2$ .

Exercises: Recognize Sequences as Functions