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10 Cards in this Set
- Front
- Back
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R1. For the sequence, 2, 6, 12, 20, 30, 42, 56, ...;
a.) Write the next two terms, telling what pattern you used. b) Draw the graph of the first six terms of the series. c) Write an equation expressing tn in terms of n. d) Use the equation to calculate t700. |
a.) the difference is 4, 6, 8, 10, 12
b.) Graph shows you it is not linear c.) n^2 + n d.) Plug it in |
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R2. Answer the following questions.
a.) Is the sequence in Problem R1 arithmetic, geometric, or neither? b.) Find t56 for the arithmetic sequence with t1 = 237 and common difference -7 c) An Arithmetic sequence has t1 = 164 and common difference -9. If tn = -484, find n. d) Find t31 for th geometric sequence with t1 = 17 and common ratio 1.2. e) A geometric sequence has t1 = 11 and common ratio 3. If tn = 24057, find n. |
a.) arithmetic needs a constant added; geometric needs a constant multiplied. So, this is neither
b.) Manipulate the formula c.) Manipulate the formula d.) Manipulate the formula e.) Manipulate the formula |
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R3. Answer the following questions.
a) Insert five arithmetic means between 17 and 63. b) Insert three geometric means between 4 and 100 if complex numbers are allowed c.) What is the geometric mean of 25 and 100 (two possible answers!)? |
a.) find the common difference and add.
b) find the common ratio and multiply. Remember there are multiple answers c.) again multiple answers |
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R4. Do the following:
a.) Evaluate Sum k=1 to 5 of k! b.) Write using sigma notation 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ... |
a.) plug and chug
b.) find a formula |
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R5. Do the following:
a.) Find S200 for the arithmetic series 6 + 13 + 20 + ... b.) 31161 is a partial sum of the series in part (a). What is the term number? c.) Find S20 for the geometric series 100+96+92.16+ ... d.) One of the partial sums of the series in part (c) is approximately 1850. Which partial sum is it? |
a) Use the equation
b) Manipulate the equation into the special form and use quadratic equation. c) Find the common ratio and plug into the equation d.) Plug in and find n |
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R6. Do the following:
a.) Find the limit to which the series in part (c) of Problem R5, above, converges. b.) Explain why the geometric series 5 + 10 + 20 + 40 + ... does not converge. c.) Write the repeating decimal 0.279279 ... as a ratio of relatively prime integers. |
a.) Use the convergent geometric series limit formula
b.) find the common ratio. The common ratio is not less than 1 c.) write as a geometric series and find common ration. then use formula to see what fraction it converges to. |
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R7. Look at the word problems in the book
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See the word problems in the book
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R8. Do the following:
a.) Evaluate 3!6!/9! b.) Write 24*23*22*21 as a ratio of two factorials.. |
a) cancel and multiply
b.) Use the trick in the book to rewrite as 24!/20! |
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R9. Expand (x - y)^4 as a binomial series.
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a.) first square it, then cube, then 4th.
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R10.
a.) Expand as a binomial series and simplify: (r^3 - 2p)^6 b.) Expand as a binomial series of complex numbers and simplify: (3 + i)^8 c.) Find the term with d^5 in the binomial series from (d + 2p)^7 d) Find the twelfth term of (t - y2_^16. Simplify. |
a.) do the math
b.) do the math c.) use the binomial theorem |
