An arithmetic series is the sum of theindicated terms of an arithmetic sequence.   4, 6, 8      arithmetic sequence   4+6+...
Find the sum: 6 + 13 + 20 + 27 + 34 + 41 + 48S7 = 6 + 13 + 20 + 27 + 34 + 41 + 48S7 = 48 + 41 + 34 + 27 + 20 + 13 + 62S7 =...
Find the sum of the first 20 even numbers, beginningwith 2.
Find the first four terms of an arithmetic series inwhich                          17 20 23 26                       14+__...
Sn = 4 + 8 + 12 + 16 + 20Sigma notation can be used to express anarithmetic seriesLast value for n           Formula for  ...
How many terms are in the series10 – 5 + 1 = 6 termsWhat are the terms   a1 = 2(5) + 3 = 13in the series?                 ...
Evaluate                       6 terms           6     6         13 23   a1 = 2(5) + 3 = 13                   6           ...
Geometric Series
If a1 + a2 + … + an is a geometric series,then the sum of the terms of the series is                        or a1 is the f...
3 + 6 + 12 + 24 + 48 + 96   a1 = 3                            r=2                            n=6                          ...
3 + 6 + 12 + 24 + 48 + 96   a1 = 3                            r=2                            n=6                          ...
3 + 6 + 12 + 24 + 48 + 96   a1 = 3                            r=2                            n=6                          ...
3 + 6 + 12 + 24 + 48 + 96   a1 = 3                            r=2                            n=6                          ...
3 + 6 + 12 + 24 + 48 + 96   a1 = 3                            r=2                            n=6                          ...
3 + 6 + 12 + 24 + 48 + 96   a1 = 3                            r=2                            n=6                          ...
3 + 6 + 12 + 24 + 48 + 96   a1 = 3                            r=2                            n=6                          ...
3 + 6 + 12 + 24 + 48 + 96   a1 = 3                            r=2                            n=6                          ...
Evaluate
Find a1 in a geometric series for whichand
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Alg2 lesson 11-2 and 11-4

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Alg2 lesson 11-2 and 11-4

  1. 1. An arithmetic series is the sum of theindicated terms of an arithmetic sequence. 4, 6, 8 arithmetic sequence 4+6+8 arithmetic series
  2. 2. Find the sum: 6 + 13 + 20 + 27 + 34 + 41 + 48S7 = 6 + 13 + 20 + 27 + 34 + 41 + 48S7 = 48 + 41 + 34 + 27 + 20 + 13 + 62S7 = 54 + 54 + 54 + 54 + 54 + 54 + 54 2S7 = 7(54) S7 = 7(54) = 189 2
  3. 3. Find the sum of the first 20 even numbers, beginningwith 2.
  4. 4. Find the first four terms of an arithmetic series inwhich 17 20 23 26 14+__+__+__+__+29=129 +d +d +d +d +d 14 14 + 5d = 29 5d = 15 d=3
  5. 5. Sn = 4 + 8 + 12 + 16 + 20Sigma notation can be used to express anarithmetic seriesLast value for n Formula for generating terms First value for n
  6. 6. How many terms are in the series10 – 5 + 1 = 6 termsWhat are the terms a1 = 2(5) + 3 = 13in the series? a2 = 2(6) + 3 = 15 a3 = 2(7) + 3 = 17 a4 = 2(8) + 3 = 19 a5 = 2(9) + 3 = 21 a6 = 2(10) + 3 = 23
  7. 7. Evaluate 6 terms 6 6 13 23 a1 = 2(5) + 3 = 13 6 a6 = 2(10) + 3 = 23 = 3(36) = 108
  8. 8. Geometric Series
  9. 9. If a1 + a2 + … + an is a geometric series,then the sum of the terms of the series is or a1 is the first term r is the common ratio n is the number of terms in the series an is the last term
  10. 10. 3 + 6 + 12 + 24 + 48 + 96 a1 = 3 r=2 n=6 an = 96
  11. 11. 3 + 6 + 12 + 24 + 48 + 96 a1 = 3 r=2 n=6 an = 96
  12. 12. 3 + 6 + 12 + 24 + 48 + 96 a1 = 3 r=2 n=6 an = 96
  13. 13. 3 + 6 + 12 + 24 + 48 + 96 a1 = 3 r=2 n=6 an = 96
  14. 14. 3 + 6 + 12 + 24 + 48 + 96 a1 = 3 r=2 n=6 an = 96
  15. 15. 3 + 6 + 12 + 24 + 48 + 96 a1 = 3 r=2 n=6 an = 96
  16. 16. 3 + 6 + 12 + 24 + 48 + 96 a1 = 3 r=2 n=6 an = 96
  17. 17. 3 + 6 + 12 + 24 + 48 + 96 a1 = 3 r=2 n=6 an = 96
  18. 18. Evaluate
  19. 19. Find a1 in a geometric series for whichand

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