Mathematics > EXAM > Chapter 9 Coursepack: Sequences, Series, and Probability Algebra 2 (All)

Chapter 9 Coursepack: Sequences, Series, and Probability Algebra 2

Document Content and Description Below

Chapter 9 Coursepack: Sequences, Series, and Probability Algebra 2 C. Bianchi, 2020 470 9.1 Introduction to Sequences Objectives: Given the formula for a sequence, find the terms and a graph. ... Given the terms in a sequence, find the formula. A sequence is a list of numbers (called the terms of the sequence). The numbers typically follow some sort of pattern. Here is an example of a sequence: 4 , 8 , 12 , 16 , 20 , 24 , … first second third term term term The first term of the sequence is denoted 1 a . The second term is called 2 a , the third term is called 3 a , and so forth. In general, the n th term in the sequence is called n a . EXAMPLE 1: Find the first four terms of the sequence n a = 3n + 8. In order to find the first term, 1 a , substitute 1 for n: 1 a = 3(1) + 8 = 3 + 8 = 11. The second term will be 2 a = 3(2) + 8 = 6 + 8 = 14. The third term will be 3 a = 3(3) + 8 = 9 + 8 = 17. The fourth term will be 4 a = 3(4) + 8 = 12 + 8 = 20. The sequence is 11, 14, 17, 20, … This sequence can be graphed by using an n-axis and an n a - axis. The graph would consist of a series of individual points representing each term in the sequence. For example, the first term ( 1 a = 11) would be plotted as the point (1 , 11). The second term ( 2 a = 14) would be plotted as the point (2 , 14). n a Notice that the points form a “linear” pattern. The graph is not technically a line because the points on a line would be connected. In this case, because the n values can only be integers (representing the number 10 of the term), the graph will only consist of individual points at n = 1, 2, 3, etc. Nonetheless, the points would all fall on the line y = 3x + 8 , which would be analogous to the sequence n a = 3n + 8. n [Show More]

Last updated: 3 years ago

Preview 1 out of 72 pages

Buy Now

Instant download

We Accept: