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Arithmetic Series

Arithmetic Series. EQ: What is an arithmetic series? How do I develop and use the formula for arithmetic series?. How do you add all of the whole numbers from 1 to 100?. 1 + 2 + 3 + … + 98 + 99 + 100. Carl Friedrich Gauss 1777-1855. How do you find S n ?.

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Arithmetic Series

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  1. Arithmetic Series EQ: What is an arithmetic series? How do I develop and use the formula for arithmetic series?

  2. How do you add all of the whole numbers from 1 to 100? 1 + 2 + 3 + … + 98 + 99 + 100 Carl Friedrich Gauss1777-1855

  3. How do you find Sn? • Sn = the sum of n terms of a series (in this case, arithmetic) Sn = u1 + u2 + u3 + … + un-2 + un-1 + un

  4. Example 1: Find the sum of the first 20 terms of the series -2 + 1 + 4 + 7 + 10…

  5. You do: For the given arithmetic sequences, find the sum, Sn, to the requested number of terms. • {4, 3, 2, …} for n = 12 • {4, 10, 16, …} for n = 15 • {2.9, 3.6, 4.3, …} for n = 11 S12 = -18 S15 = 690 S11 = 70.4

  6. Example 2: An arithmetic series has a 3rd term of 0. The sum of the first 15 terms is -300. What is the 1st term and the sum of the first ten terms?

  7. Example 3: A new business is selling home computers. They predict they will sell 20 computers in their 1st month, 23 in the 2nd month, 26 in the 3rd, and so on, in arithmetic sequence. How many months will pass before the company expects to sell their thousandth computer?

  8. YOU DO: Each day a runner trains for a 10 km race. On the first day she runs 1000 m, and then increases the distance by 250 m on each subsequent day. (a) On which day does she run a distance of 10 km in training? (b) What is the total distance she will have run in training by the end of that day? Give your answer exactly.

  9. -105 You do: Find the sum of the following sequences: (a) {5, 4, 3, …, -15} (b) {3, 9, 15, … , 75} (c) {3, 5, 7, … ,29} 507 224

  10. Sequences, Series & Your GDC BASIC: u1 = 5 and d = 7 Type 5 ENTER. Type + 7, then ENTER ENTER ENTER…

  11. Changing the Mode • Hit MODE – Change from Func to Seq. • Go to Y = Notice you have u(n), v(n) and w(n). You can type all of these in on your main screen by typing 2nd 7, 8, or 9. Example: un = 127 – 7n. Type into u(n). Find u(15). Check out your table and plot it.

  12. Storing a List • Type 2nd 0 LN (s). Then find seq( and hit ENTER. Type in seq(6 + 4n, n, 1, 8). This will list the terms of the sequence from u1 to u8. • Hit STO  2nd STAT L1 ENTER • Then type 2nd 0 4(T) STAT L1 ENTER • Your answer should be 192.

  13. Ticket Out the DoorCreate your own word problem that involves calculating an arithmetic series.

  14. Homeworkp. 186-188 #3, 5, 7-12

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