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Introduction to Sequences. Essential Questions. How do we find the nth term of a sequence? How do we write rules for sequences? How do we evaluate summation notation?. Holt McDougal Algebra 2. Holt Algebra 2.
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Introduction to Sequences Essential Questions • How do we find the nth term of a sequence? • How do we write rules for sequences? • How do we evaluate summation notation? Holt McDougal Algebra 2 Holt Algebra 2
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 sequenceis an ordered set of numbers. Each number in the sequence is a term of the sequence. A sequence may be an infinite sequencethat continues without end, such as the natural numbers, or a finite sequencethat has a limited number of terms, such as {1, 2, 3, 4}.
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 a1 = 1, a2 = 1, and an= an – 2 + an – 1, where n ≥ 3. This is a recursive formula. A recursive formulais a rule in which one or more previous terms are used to generate the next term.
Finding Terms of a Sequence Write the first five terms of the sequence. 10, 8, 6, 4, 2
Finding Terms of a Sequence Write the first five terms of the sequence.
In some sequences, you can find the value of a term when you do not know its preceding term. An explicit formuladefines the nth term of a sequence as a function of n.
Finding Terms of a Sequence Write the first five terms of the sequence. Start with n = 1. 2, 7, 12, 17, 22
Finding Terms of a Sequence Write the first five terms of the sequence. Start with n = 1.
Finding Terms of a Sequence Write the first five terms of the sequence. Start with n = 1. -1, 0, 3, 8, 15
Remember! Linear patterns have constant first differences. Quadratic patterns have constant second differences. Exponential patterns have constant ratios.
Writing Rules for Sequences Write the next term in the sequence. Then write a rule for the nth term.
Writing Rules for Sequences Write the next term in the sequence. Then write a rule for the nth term.
Writing Rules for Sequences Write the next term in the sequence. Then write a rule for the nth term.
Writing Rules for Sequences Write the next term in the sequence. Then write a rule for the nth term. -2 -2 -2
