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Mathematics, Grade 8

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Study Guide Sequences Mathematics, Grade 8

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SEQUENCES What Are Sequences? A sequence is an ordered list of numbers. Sequences are the result of a pattern or rule. A pattern or rule can be every other number or some formula such as y = 2x + 3. • When a pattern or rule is given, a sequence can be found. • When a sequence is given, the pattern or rule can be found. Sequences can be arithmetic or geometric. • An arithmetic sequence contains numbers. • A geometric sequence contains figures or numbers based on geometric shape such as perimeters, areas or volumes. Sometimes, a pattern is written in words and a sequence is needed. Another example of number patterns is a word problem. In this case, a pattern would have to be figured out so the answer to the problem can be given. How to use sequences Sequences can be used to determine a pattern or rule. This can also be related to functions, where for each x, a rule is followed to produce a result, y. For the following sequence, 5, 6, 7, 8, 9, 10, what is the pattern? Since the sequence starts at 5 and continues with each consecutive number, the rule is x + 5 when x starts at 0. When an arithmetic sequence is given and asked for the next three numbers, the first step is to look at the numbers for some kind of relationship. A common pattern used is numbers that are multiples of a number. Once a pattern is established, follow the pattern to give the next numbers. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

In the example below, what are the next three numbers? Ex. 1, 1, 2, 3, 5, 8, 13, ___, ___, ___... → 21, 34, and 55 The pattern is that each number equals the addition of the two previous numbers. The next three numbers are 21, 34 and 55. This sequence is called the Fibonacci sequence because it was first described by Leonardo Fibonacci. If the pattern is given, simply follow the pattern to find the numbers in the sequence. Geometric sequences contain figures or information with regards to figures. For example, the volume of cubes is in a sequence of 1 m³, 8 m³, 27 m³…if this pattern continues, what is the volume of a cube with sides 6 m long? Ex. The sequence is 1, 8, 27, 64, 125, 216… or x³ Based on the sequence, the volume of a cube with sides 6 m long would be 216 m³. Word problems also can be used with sequences. With a word problem, the pattern must be figured out in order to answer the problem. For example, a teacher is picking students in her class to do an experiment. She has the students line up in a row. She picks the first student, then the fourth student, then the ninth student and so on. If there are 29 students in the class, how many were picked? Ex. The sequence is 1, 4, 9, 16, 25, 36… Since there are 29 students in the class, the teacher picked the first, fourth, ninth, sixteenth and twenty- fifth students for a total of 5 students. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! 1. What is the pattern of the sequence: 2, 4, 6, 8, 10…? 2. What is the pattern of the sequence: 0, 1, 1, 2, 4, 8, 16…? 3. What are the next three numbers of the sequence: -1, 0, 3, 8…? 4. If the pattern starts at 3 and the pattern is x + 8, what are the first four numbers in the sequence? 5. If the perimeter of a figure increases by four with every two blocks that are added and the first block has a perimeter of 4, what is the perimeter of a figure with 5 blocks? 6. A musician is playing notes on a piano; he plays the first key, the fifth key, tenth key and so on. If there are 88 keys on his piano, how many keys did he play? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Sequences

Mathematics, Grade 8

Sequences

Study Guide

Sequences

Flash Cards

Sequences

Quiz

Sequences

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Sequences

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Study Guide Sequences Mathematics, Grade 8

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