Presentation on theme: "What are two types of Sequences?"— Presentation transcript:
1 What are two types of Sequences? What is a sequence?A sequence of numbers is a list, an ordering that may or may not follow some rule.What are two types of Sequences?Arithmetic Sequence:Geometric Sequence:Is a sequence in which each term is equal to the previous term plus a constant. This constant is called the common difference.Is a sequence in which each term is equal to the previous term multiplied by a constant. This constant is called the common ratio.
2 When we are given a sequence and asked to find a specific term… 1.Determine whether the sequence is arithmetic or geometric.2. Find the common difference (arithmetic) or the common ratio (geometric)3. Use the appropriate formula to find the term asked for.Arithmetic Geometric
3 We will be reviewing arithmetic Find the common difference, find the indicated term, write the equation in both function and explicit formLet’s look at a sequence.12, 6, 0, -6, FindWrite down every thing you need in the formula.n =10 because we are looking for the 10th termd = -6 because we are adding -6 to each term= 12 because it is the first term of the sequence
4 Now use the information in the formula…don’t plug in “n” and you will have the explicit form This is the explicit formDistribute the -6 and simplify, change to f(n) and you will have function formThis is function formTo find the 10th term use n = 10 and simplify
5 So let’s list some steps First find the common differenceNext list all of the unknownsFind the explicit form by plugging in the first term and the common differenceFind the function form by simplifying the explicit formTo find the specific term replace n with the term you are looking for.
6 You try…Find the common difference, the indicated term, write the explicit and function form of the sequence.6,106, 206, 306,…n=15-38,-45,-52,-59,…n=23-16,14, 44, 74,…n=521406-2061574
7 What is a recursive sequence? Definition: A recursive sequence is the process in which each step of a pattern is dependent on the step or steps before it.Recursion Formulas:A recursion formula defines the nth term of a sequence as a function of the previous term. If the first term of a sequence is known, then the recursion formula can be used to determine the remaining terms.
8 Let’s look at the following sequence Sequence and TermsLet’s look at the following sequencen²Do you know what the rule is for the sequence?1,4,9,16,25,36,49,…,The letter a with a subscript is used to represent function values of a sequence.The subscripts identify the location of a term.
9 How to read the subscripts: a term in the sequencethe priortermthe next term
10 Example 1: Find the first four terms of the sequence: General TermLet’s be sure we understand what is given+ 2isEach term after the first3 times the previous termThe first term is 5Plus 2
11 Continued… EX 1: Find the first four terms of the sequence: Start with general term for n>1n=1givenn=2n=3n=4Answer = 5, 17, 53, 161
12 Your turn: Ex 2: Find the next four terms of the sequence. Start with general term for n>1n=1givenn=2n=3n=4Answer = 3, 6, 12, 24
13 Write a recursive formula for the arithmetic sequence below Write a recursive formula for the arithmetic sequence below. Step 1 : Make sure it is arithmetic Step 2 : Plug into the arithmetic recursive formula. Step 3 : Make sure you tell us what a1 is equal to.Ex. 37, 3, -1, -5, -9, …The common difference = -4The first term = 7
14 Choose the recursive formula for the given sequence. Last Example Choose the recursive formula for the given sequence.Answer = C