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Arithmetic & Sequences

Mathematics, Grade 8

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• A sequence is a set of numbers, called terms, in a specific order. • An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant. This difference which increases or decreases by a constant amount each term is called the common difference. • The common difference is either added or subtracted to each term to determine the next term. The common difference is: This geometric sequence has a common ratio of 2. Find the 12th term of the sequence Find the 12th term of the sequence Example: Example: Example: Example: • To determine the nth term (an) of an arithmetic sequence with a common difference (d), the following formula may be used: • A geometric sequence is a sequence in which each term after the first is multiplied by a constant to obtain the following term. • The constant multiplier is called the common ratio (r). • To determine the nth term (an) of a geometric sequence with a common ratio (r), the following formula may be used: Finding the nth Term of an Arithmetic Sequence Finding the nth Term of a Geometric Sequence 3 3 3 3 3 3, 6, 12, 15, 18... 15 – 12 = 3 9, 3, 6, 9, 12, 15, 18... an = a1 + (n – 1)d a12 = a1 + (12 – 1)3 a12 = 36 an = a1 r n - 1 3, 6, 12, 24, 48, 96... a 12 = 3 • 2 12 – 1 a 12 = 3 • 2 11 a 12 = 3 • 2,048 a 12 = 6,144 2 2 2 2 ratio 2 = 1 2 3, 6, 24, 48, 96... 12, Arithmetic Sequences Geometric Sequences © Copyright NewPath Learning. All Rights Reserved. 93-4809 www.newpathlearning.com Arithmetic & Geometric Sequences

• A sequence is a _____________________ _____________________________________. • An arithmetic sequence is a sequence in which the difference between any two consecutive terms is . This difference which increases or decreases by a constant amount each term is called the . • The common difference is either or to each term to determine the next term. The common difference is: This geometric sequence has a common ratio of . Find the 12th term of the sequence Find the 12th term of the sequence Example: Example: Example: Example: • To determine the nth term (an) of an arithmetic sequence with a common difference (d), the following formula may be used: • A geometric sequence is a sequence in which each term after the first is multiplied by a constant to obtain the following term. • The constant multiplier is called the common ratio (r). • To determine the nth term (an) of a geometric sequence with a common ratio (r), the following formula may be used: Finding the nth Term of an Arithmetic Sequence Finding the nth Term of a Geometric Sequence 3, 6, 12, 15, 18... 15 – 12 = 3 9, 3, 6, 9, 12, 15, 18... an = a1 + (n – 1)d an = a1 r n - 1 3, 6, 12, 24, 48, 96... ratio = 3, 6, 24, 48, 96... 12, Arithmetic Sequences Geometric Sequences a12 = a12 = a12 = © Copyright NewPath Learning. All Rights Reserved. 93-4809 www.newpathlearning.com Arithmetic & Geometric Sequences Key Vocabulary Terms • arithmetic sequence • common difference • common ratio • constant • geometric sequence • sequence • term \|xiBAHBDy01666tz]

Arithmetic & Sequences

Mathematics, Grade 8

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