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12.2 – Analyze Arithmetic Sequences and Series

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Arithmetic Sequence: The difference of consecutive terms is constant Common Difference: d, the difference between any two terms

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1. Tell whether the sequence is arithmetic. –4, 1, 6, 11, 16, … +5 Yes +5 a.

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1. Tell whether the sequence is arithmetic. 3, 5, 9, 15, 23, … +2+4+6+8 No b.

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1. Tell whether the sequence is arithmetic. 17, 14, 11, 8, 5,… –3 Yes –3 c.

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Rule for an Arithmetic Sequence The nth term of an arithmetic sequence with first term a 1 and common difference d is given by:

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2.Write a rule for the nth term of the sequence. Then find a 15. 4, 9, 14, 19, … +5 a. d = 5 a1 =a1 = 4

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2.Write a rule for the nth term of the sequence. Then find a 15. 60, 52, 44, 36, … –8 b. d = –8 a1 =a1 = 60

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3. Write a rule for the nth term of the sequence given: d = 3, a 19 = 48

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4. Write a rule for the nth term of the sequence given: d = –7, a 11 = –57

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5. Write a rule for the nth term of the sequence given: a 8 = 21, a 27 = 97 –1

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6. Write a rule for the nth term of the sequence given: a 7 = 26, a 16 = 71 –1

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Arithmetic Series: Adding the terms of an arithmetic sequence

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Sum of a Finite Arithmetic Series: The sum of the first n terms is:

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7. What is the sum of the arithmetic series? a1 =a1 = 3+5(1) a1 =a1 = 8 a 20 = 3+5(20) a 20 = 103 n = 20

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8. What is the sum of the arithmetic series? a4 =a4 = 6(4) – 30 a4 =a4 = –6 a9 =a9 = 6(9) – 30 a 20 = 24 n = 6

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9. What is the sum of the arithmetic series? a8 =a8 = – 11 + 4(8) a8 =a8 = 21 a 16 = – 11 + 4(16) a 16 = 53 n = 9

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10. What is the sum of the arithmetic series? a1 =a1 = 5 an =an = 203 d = 2

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11. What is the sum of the arithmetic series? a1 =a1 = 2 an =an = 198 d =7

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