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ARITHMETIC  SERIES
Examine the following sequence: 3,6,12,24,48,96,… 1,1,2,3,5,8,13,21,…
Examine the following sequence:   3,6,12,24,48,96,…      The succeeding term is two times               the previous term....
Examine the following sequence: 1,1,2,3,5,8,13,21,…     The succeeding term is the sum            of the two previous term...
ARITHMETIC  SERIES
“The GSC Water District will impose a newminimum charge of P150 for first 10 cubic meters and additional charge of P20 for...
WATER CHARGE MATRIX      Water  Consumption     Charge in Pesos   (cu. meters)   10 or less          150       11       12...
WATER CHARGE MATRIX      Water  Consumption     Charge in Pesos   (cu. meters)   10 or less          150       11         ...
WATER CHARGE MATRIX      Water  Consumption     Charge in Pesos   (cu. meters)   10 or less          150       11         ...
WATER CHARGE MATRIX      Water  Consumption     Charge in Pesos   (cu. meters)   10 or less          150       11         ...
WATER CHARGE MATRIX      Water  Consumption     Charge in Pesos   (cu. meters)   10 or less          150       11         ...
WATER CHARGE MATRIX      Water  Consumption     Charge in Pesos   (cu. meters)   10 or less          150       11         ...
Study the following sequence. 1, 2, 3, 4, 5,… 0, 5, 10, 15, 20, 25,… 5, 2, -1, -4, -7, -10,…
1, 2, 3, 4, 5,…         •The terms are obtain by               adding 1 to each               succeeding terms.
0, 5, 10, 15, 20, 25,…              •The terms are obtain by                    adding 5 to each                   succeed...
5, 2, -1, -4, -7, -10,…      •The terms are obtain by            adding –3 to each            succeeding terms.or example ...
Definition: Arithmetic Sequence       An arithmetic sequence is asequence in which each term after thefirst is obtained by...
1, 2, 3, 4, 5,…          •The terms are obtain by                adding 1 to each                succeeding terms.The comm...
0, 5, 10, 15, 20, 25,…                •The terms are obtain by                      adding 5 to each                     s...
5, 2, -1, -4, -7, -10,…        •The terms are obtain by              adding –3 to each              succeeding terms.The c...
The common difference, d , of an arithmetic sequence:The nth term of an arithmetic sequence:
Illustrative Problem 1:     Complete the arithmeticsequence,           , up to 8 terms.Solution: Let       ,      ,       ...
The first 8 terms of the sequence, using                                , are…  The first 8 terms of the sequence are…
Illustrative Problem 2: Find the       25th                term of the arithmetic series 2, 5, 8, 11, …
Illustrative Problem 3:  Find the arithmeticseries of 6 terms if thefirst term is 27 and thelast term is 12.
Assignment:   Solve the following problems   1. What are the first three terms of the arithmetic      series whose 9th ter...
ARITHMETIC  SERIES
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Sequence powerpoint

  1. 1. ARITHMETIC SERIES
  2. 2. Examine the following sequence: 3,6,12,24,48,96,… 1,1,2,3,5,8,13,21,…
  3. 3. Examine the following sequence: 3,6,12,24,48,96,… The succeeding term is two times the previous term.For example the 2ndterm: 6 = 3G2
  4. 4. Examine the following sequence: 1,1,2,3,5,8,13,21,… The succeeding term is the sum of the two previous term.For example the 6th term is: 8 = 5+3
  5. 5. ARITHMETIC SERIES
  6. 6. “The GSC Water District will impose a newminimum charge of P150 for first 10 cubic meters and additional charge of P20 for every cubic meter in excess of the minimum effective June 2011…”Read the information above and complete thecharge matrix below if you want to know howmuch will be charged on your water bill.
  7. 7. WATER CHARGE MATRIX Water Consumption Charge in Pesos (cu. meters) 10 or less 150 11 12 13 14 15
  8. 8. WATER CHARGE MATRIX Water Consumption Charge in Pesos (cu. meters) 10 or less 150 11 170 12 13 14 15
  9. 9. WATER CHARGE MATRIX Water Consumption Charge in Pesos (cu. meters) 10 or less 150 11 170 12 190 13 14 15
  10. 10. WATER CHARGE MATRIX Water Consumption Charge in Pesos (cu. meters) 10 or less 150 11 170 12 190 13 210 14 15
  11. 11. WATER CHARGE MATRIX Water Consumption Charge in Pesos (cu. meters) 10 or less 150 11 170 12 190 13 210 14 230 15
  12. 12. WATER CHARGE MATRIX Water Consumption Charge in Pesos (cu. meters) 10 or less 150 11 170 12 190 13 210 14 230 15 250
  13. 13. Study the following sequence. 1, 2, 3, 4, 5,… 0, 5, 10, 15, 20, 25,… 5, 2, -1, -4, -7, -10,…
  14. 14. 1, 2, 3, 4, 5,… •The terms are obtain by adding 1 to each succeeding terms.
  15. 15. 0, 5, 10, 15, 20, 25,… •The terms are obtain by adding 5 to each succeeding terms.
  16. 16. 5, 2, -1, -4, -7, -10,… •The terms are obtain by adding –3 to each succeeding terms.or example the2nd term: 2 = 5+ (-3)
  17. 17. Definition: Arithmetic Sequence An arithmetic sequence is asequence in which each term after thefirst is obtained by adding the samefixed number, called the commondifference, to the preceding term.
  18. 18. 1, 2, 3, 4, 5,… •The terms are obtain by adding 1 to each succeeding terms.The common difference is d=1
  19. 19. 0, 5, 10, 15, 20, 25,… •The terms are obtain by adding 5 to each succeeding terms.The common difference is d=5
  20. 20. 5, 2, -1, -4, -7, -10,… •The terms are obtain by adding –3 to each succeeding terms.The common difference is d = -3
  21. 21. The common difference, d , of an arithmetic sequence:The nth term of an arithmetic sequence:
  22. 22. Illustrative Problem 1: Complete the arithmeticsequence, , up to 8 terms.Solution: Let , , .Then the common difference is
  23. 23. The first 8 terms of the sequence, using , are… The first 8 terms of the sequence are…
  24. 24. Illustrative Problem 2: Find the 25th term of the arithmetic series 2, 5, 8, 11, …
  25. 25. Illustrative Problem 3: Find the arithmeticseries of 6 terms if thefirst term is 27 and thelast term is 12.
  26. 26. Assignment: Solve the following problems 1. What are the first three terms of the arithmetic series whose 9th term is 16 and 40th term is 47? 2. The 18th and 52nd terms of an arithmetic series are 3 and 173, respectively. Find the 25th term. 3. Find the sum of all odd integers from 27 to 495, inclusive. 4. What is the value of k such that , , and forms an arithmetic series?
  27. 27. ARITHMETIC SERIES

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