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**8.2 Arithmetic Sequences and Series 8.3 Geometric Sequences and Series**

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Arithmetic Sequences A sequence is arithmetic if the differences between consecutive terms are the same. So, the sequence a1, a2, a3, ….,an is arithmetic if there is a number d such that a2-a1= a3-a2=a4-a3=…=d The number d is the common difference of the sequence.

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Examples

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**nth Term of an Arithmetic Sequence**

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More examples The fourth term of an arithmetic sequence is 20, and the 13th term is 65. What is the nth term of the sequence? Find the tenth term of the arithmetic sequence that begins with 8 and 20.

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**Sum of a Finite Arithmetic Sequence**

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Exercises: Determine the seating capacity of an auditorium with 30 rows of seats if there are 20 seats in the first row, 22 seats in the second row, 24 in the third row and so on. Can you find the sum of an infinite arithmetic series?

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Geometric Sequences A sequence is geometric if the ratios of consecutive terms are the same. So, the sequence a1, a2, a3, ….,an is geometric if there is a number r such that a2/a1= a3/a2=a4/a3=…=r The number r is the common ratio of the sequence.

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Examples

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**nth Term of an Geometric Sequence**

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More examples Find the nth term of a geometric sequence whose first term is 4 and whose common ratio is ½ . The second term of a geometric sequence is -18 and the fifth term is 2/3. Find the sixth term.

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**The Sum of a Finite Geometric Sequence**

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**Sum of an Infinite Geometric Series**

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More examples Find the sum .

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Aim: What are the arithmetic series and geometric series? Do Now: Find the sum of each of the following sequences: a) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15.

Aim: What are the arithmetic series and geometric series? Do Now: Find the sum of each of the following sequences: a) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15.

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