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9.2 Arithmetic Sequences and Series
An arithmetic sequence is a sequence in which each term is obtained by adding a fixed number to the previous term. 5, 9, 13, 17 … is an example of an arithmetic sequence since 4 is added to each term to get the next term. The fixed number added is called the common difference.
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9.2 Finding a Common Difference
Example Find the common difference d for the arithmetic sequence –9, –7, –5, –3, –1, … Solution d can be found by choosing any two consecutive terms and subtracting the first from the second: d = –5 – (–7) = 2 .
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9.2 Arithmetic Sequences and Series
nth Term of an Arithmetic Sequence In an arithmetic sequence with first term a1 and common difference d, the nth term an, is given by
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9.2 Finding Terms of an Arithmetic Sequence
Example Find a13 and an for the arithmetic sequence –3, 1, 5, 9, … Solution Here a1= –3 and d = 1 – (–3) = 4. Using n=13, In general
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9.2 Find the nth term from a Graph
Example Find a formula for the nth term of the sequence graphed below.
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9.2 Find the nth term from a Graph
Solution The equation of the dashed line shown Below is y = –.5x +4. The sequence is given by an = –.5n +4 for n = 1, 2, 3, 4, 5, 6 .
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9.2 Arithmetic Sequences and Series
Sum of the First n Terms of an Arithmetic Sequence If an arithmetic sequence has first term a1 and common difference d, the sum of the first n terms is given by or
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9.2 Using The Sum Formulas Example Find the sum of the first 60 positive integers. Solution The sequence is 1, 2, 3, …, 60 so a1 = 1 and a60 = 60. The desired sum is
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9.2 Using Summation Notation
Example Evaluate the sum . Solution The sum contains the terms of an arithmetic sequence having a1 = 4(1) + 8 = 12 and a10 = 4(10) + 8 = 48. Thus,
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