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Arithmetic Sequences and Series

Arithmetic Sequences and Series. Sequences. Series. “Indicated sum”. List with commas. 3, 8, 13, 18. 3 + 8 + 13 + 18. Arithmetic Sequence. Arithmetic Sequence – a sequence whose consecutive terms have a common difference(or slope).

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Arithmetic Sequences and Series

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  1. Arithmetic Sequences and Series

  2. Sequences Series “Indicated sum” List with commas 3, 8, 13, 18 3 + 8 + 13 + 18

  3. Arithmetic Sequence Arithmetic Sequence– a sequence whose consecutive terms have a common difference(or slope). So the sequence is arithmetic if there is a number d such that The # d is the common difference.

  4. nth term Finding the nth term of an Arithmetic Sequence an = a1 + d(n – 1)

  5. Alternative Formula an = dn + a0

  6. Ex. 1 Find the equation 7, 11, 15, 19, …, 2, -3, -8, -13, …, 1, 4, 9, 16, ….. (not arithmetic)

  7. Ex. Find the 68th term in the sequence 16, 7, -2, . . . 68 7-16 = -9 = -587 16

  8. Ex. 2 Find a formula for: a1 = 2 and d = 3 an = 3n – 1 2, 5, 8, 11, 14, 17, 20, …

  9. The 4th term of an arithmetic sequence is 20 and the 13th term is 65. Find the first five terms of this sequence. Ex. 3

  10. The 4th term of an arithmetic sequence is 20 and the 13th term is 65. Find the first five terms of this sequence. Ex. 3 5, 10, 15, 20, 25, 30, 35, …

  11. Add up all the numbers from 1 to 100

  12. Add up all the numbers from 1 to 100 5050

  13. 1 + 2 + 3 + 4 + …+ 49 + 50 + 51 + 52 … + 97 + 98 + 99 + 100 What do each of these pairs sum to? 101 How many pairs do you have? 50 = the number of terms you have, divided by two 50 (101)

  14. Sum of a finite arithmetic series

  15. Find the sum of the first 27 terms in the series: –14 – 8 – 2 - . . . Ex.5b 27 -14 142

  16. Find the 32nd partial sum of the series: 0.5+0.75+1 + … Ex. 7b an = a1 + d(n – 1) a32 = 0.5 + d(32 – 1) a32 = 0.5 + 0.25(32 – 1) 8.25

  17. Find the 32nd partial sum of the series: 0.5+0.75+1 + … Ex. 7b 8.25

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