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Warmup 3/11/14

Warmup 3/11/14. Spend the first 5 minutes of class each day looking through the homework so you can either help each other or ask Mr. C. to go through a problem on the board as a class. Objective Tonight’s Homework. To define a series for arithmetic and geometric sequences.

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Warmup 3/11/14

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  1. Warmup3/11/14 Spend the first 5 minutes of class each day looking through the homework so you can either help each other or ask Mr. C. to go through a problem on the board as a class. Objective Tonight’s Homework To define a series for arithmetic and geometric sequences pp 589: 1, 5, 6, 9, 10, 11, 13

  2. Homework Help Let’s spend the first 10 minutes of class going over any problems with which you need help.

  3. Notes on Series’ We studied arithmetic and geometric sequences. In an arithmetic sequence, the numbers increase by adding or subtracting the same amount each time. In a geometric sequence, the numbers increase by multiplying or dividing the same amount each time.

  4. Notes on Series’ We studied arithmetic and geometric sequences. In an arithmetic sequence, the numbers increase by adding or subtracting the same amount each time. In a geometric sequence, the numbers increase by multiplying or dividing the same amount each time. An arithmetic or geometric series is the same as a sequence except we add together each value to get a single total number in a given span.

  5. Notes on Series’ Example: Find the series for the first 8 terms of the sequence below: 11, 14, 17, 20, 23, 26, 29, 32 We want to develop a formula we can use for all arithmetic series.

  6. Notes on Series’ Example: Find the series for the first 8 terms of the sequence below: 11, 14, 17, 20, 23, 26, 29, 32 We want to develop a formula we can use for all arithmetic series. If we look closely, we’ll notice that adding terms from both ends inward always results in the same total. 11 + 32 = 43 14 + 29 = 43 17 + 26 = 43

  7. Notes on Series’ So how does this help? Well, we’re essentially doing this: 8/2 • (first term + last term)

  8. Notes on Series’ So how does this help? Well, we’re essentially doing this: 8/2 • (first term + last term) We’re adding up how many terms we have, dividing by 2 (since we’re working with pairs), then multiplying by how big each pair is.

  9. Notes on Series’ So how does this help? Well, we’re essentially doing this: 8/2 • (first term + last term) We’re adding up how many terms we have, dividing by 2 (since we’re working with pairs), then multiplying by how big each pair is. Or to generalize further… arithmetic series = n/2 • (first term + last term)

  10. Notes on Series’ We can do a similar (although more difficult) process with our geometric sequences to get… geometric series = (first term)(1 – rn)/ (1 – r) Where: r is the common ratio n is the number of terms you want to sum

  11. Notes on Series’ Example: Find the sum of the first 9 terms in a geometric series whose first term is -8 and whose common ratio is -2.

  12. Notes on Series’ Example: Find the sum of the first 9 terms in a geometric series whose first term is -8 and whose common ratio is -2. Series = (first term)(1 – rn) / (1 – r) Series = (-8)(1 – (-2)9) / (1 – -2) Series = (-8)(1- (-512))/3 Series = (-4104)/3 Series = -1368

  13. Group Practice Look at the example problems on pages 587 to 589. Make sure the examples make sense. Work through them with a friend. Then look at the homework tonight and see if there are any problems you think will be hard. Now is the time to ask a friend or the teacher for help! pp 589: 1, 5, 6, 9, 10, 11, 13

  14. Exit Question #40 What do we get if we sum up the integers 0 through 100? a) 500 b) 1111 c) 2500 d) 3000 e) 5050 f) None of the above

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