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Arithmetic Sequences & Series

Arithmetic Sequences & Series. Pre-Calculus Section. It is an “ Arithmetic Sequence ” when the same number is added to get from one term to the next. The number being added is called the common difference (d) . To find the common difference, subtract any two consecutive terms.

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Arithmetic Sequences & Series

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  1. Arithmetic Sequences & Series Pre-Calculus Section

  2. It is an “Arithmetic Sequence” when the same number is added to get from one term to the next. The number being added is called the commondifference (d). To find the common difference, subtract any two consecutive terms. To find d: ( a2 - a1), or (a3 - a2), or (a4 - a3), etc. 1. 18, 12, 6, 0, - 6,… d = __ - 6 2. - 13, - 6, 1, 8, … d = __ 7

  3. Decide if each series is an arithmetic series.If so, find the common difference. 1) Yes, difference = 4. No common difference. 2) No common difference. 3) Yes, difference = -4. 4)

  4. If the 1st term of an arithmetic sequence is 10,& the common difference is 3, find the next 4 terms. a1 = 10 a2 = _____ = __ 10 + d 13 13 + d 16 a3 = ______ = __ a4 = __ 19 a5 = __ 22 13, 16, 19, 22 If the first term of an arithmetic sequence is 6, & the common difference is -2, find the first 4 terms. 4 0 a1 = __, a2 = __, a3 = __, a4 = __ 6 2 6, 4, 2, 0

  5. an= a1 + (n - 1)d a41 = ____ d = __ a1 = __ n = __ Formula to find aspecific term: an = the term to be found Memorize This Formula! a1 = 1st term n = number of terms d = common difference Given the sequence: 8, 5, 2, - 1, …, find the 41st term. 8 41 - 3 - 112 a41 =_________ 8 + 40 (- 3)

  6. an= a1 + (n - 1)d an= a1 + (n - 1)d Find the 15th term of the sequence: 6, 3, 0, … a1 = __; d = __; n = __ - 3 15 6 a15 = _________ = ____ - 36 6 + 14(- 3) In an arithmetic sequence, a1 = 2; d = 3; find a10 a1 = __; d = __; n = __ 2 3 10 a10 = _______ = ___ 2 + 9(3) 29

  7. an= a1 + (n - 1)d

  8. 1) 2)

  9. an= a1 + (n - 1)d Need to know the 1st term. Find it first!

  10. an= a1 + (n - 1)d

  11. an= a1 + (n - 1)d

  12. Sum of a Finite Arithmetic Sequence To use this formula, you must know the first and the last term. Alternate Formula To use this formula, you must know the first term and the common difference.

  13. n = 20 a1 = 12 d = 6

  14. an= a1 + (n - 1)d Find the 50th term.

  15. an= a1 + (n - 1)d We don’t know how many terms are being added! First find what term 38 is. 38 = 3 + (n – 1)5 38 = 3 + 5n – 5 38 = 5n – 2 40 = 5n 8 = n It’s the 8th term!

  16. an= a1 + (n - 1)d Formulas to Memorize! Write the formula at the beginning of each problem. You will have it memorized by the time you finish the homework.

  17. Homework Page

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