Introductiontoto Sequences How do we find the nth

Introductiontoto. Sequences • How do we find the nth term of a sequence? • How do we write rules for sequences? • How do we evaluate summation notation? Holt. Mc. Dougal Algebra 2 Holt

Introduction to Sequences In 1202, Italian mathematician Leonardo Fibonacci described how fast rabbits breed under ideal circumstances. Fibonacci noted the number of pairs of rabbits each month and formed a famous pattern called the Fibonacci sequence. A sequence is an ordered set of numbers. Each number in the sequence is a term of the sequence. A sequence may be an infinite sequence that continues without end, such as the natural numbers, or a finite sequence that has a limited number of terms, such as {1, 2, 3, 4}. Holt Mc. Dougal Algebra 2

Introduction to Sequences In the Fibonacci sequence, the first two terms are 1 and each term after that is the sum of the two terms before it. This can be expressed by using the rule a 1 = 1, a 2 = 1, and an = an – 2 + an – 1, where n ≥ 3. This is a recursive formula. A recursive formula is a rule in which one or more previous terms are used to generate the next term. Holt Mc. Dougal Algebra 2

Introduction to Sequences Finding Terms of a Sequence Write the first five terms of the sequence. 10, 8, 6, 4, 2 Holt Mc. Dougal Algebra 2

Introduction to Sequences Finding Terms of a Sequence Write the first five terms of the sequence. Holt Mc. Dougal Algebra 2

Introduction to Sequences In some sequences, you can find the value of a term when you do not know its preceding term. An explicit formula defines the nth term of a sequence as a function of n. Holt Mc. Dougal Algebra 2

Introduction to Sequences Finding Terms of a Sequence Write the first five terms of the sequence. Start with n = 1. 2, 7, 12, 17, 22 Holt Mc. Dougal Algebra 2

Introduction to Sequences Finding Terms of a Sequence Write the first five terms of the sequence. Start with n = 1. Holt Mc. Dougal Algebra 2

Introduction to Sequences Finding Terms of a Sequence Write the first five terms of the sequence. Start with n = 1. -1, 0, 3, 8, 15 Holt Mc. Dougal Algebra 2

Introduction to Sequences Remember! Linear patterns have constant first differences. Quadratic patterns have constant second differences. Exponential patterns have constant ratios. Holt Mc. Dougal Algebra 2

Introduction to Sequences Writing Rules for Sequences Write the next term in the sequence. Then write a rule for the nth term. Holt Mc. Dougal Algebra 2

Introduction to Sequences Writing Rules for Sequences Write the next term in the sequence. Then write a rule for the nth term. Holt Mc. Dougal Algebra 2

Introduction to Sequences Writing Rules for Sequences Write the next term in the sequence. Then write a rule for the nth term. Holt Mc. Dougal Algebra 2

Introduction to Sequences Writing Rules for Sequences Write the next term in the sequence. Then write a rule for the nth term. -2 Holt Mc. Dougal Algebra 2 -2 -2

Introduction to Sequences Lesson 5. 1 Practice A Holt Mc. Dougal Algebra 2