The document discusses different types of sequences including arithmetic and geometric sequences. It provides examples of explicit and recursive definitions for sequences. Specifically, it gives the first six terms of the sequence defined by the formula in the problem and examples of explicit and recursive definitions for arithmetic sequences with a first term and constant difference and geometric sequences with a first term and constant ratio.

1. Sequences Warm-Up Write the first six terms of the sequence with the given formula:

2. Sequences Sequences are functions whose domain is a set of consecutive integers greater than or equal to k . For Example, if Then the function R contains the points (1,2), (2,6), (3,12), (4,20), (5,30), etc… There are two ways to define R: Explicit Recursive

3. Given Write the first 5 terms of the sequence: Write a recursive formula for the sequence:

4. is an example of an arithmetic sequence. ( p. 490 ) Arithmetic sequences are sequences in which the difference between consecutive terms is a constant. To generate an arithmetic sequence with first term a 1 and constant difference d , Explicit Recursive Is this the same as what we used for b n ?

5. ( p. 491 ) Another type of sequence is a geometric sequence. Geometric sequences are sequences in which the ratio of consecutive terms is constant. For example, the sequence 2, 4, 8, 16, 32, 64,… is a geometric sequence where the constant ratio is 2:1. What is the constant ratio in the sequence 2, 3, 4.5, 6.75, 10.125,…? To generate a definition for a geometric sequence with first term g 1 and constant ratio r : Explicit Recursive