Sequences and Series Project Patterns occur everywhere in life especially in mathematics. A pattern can be defined as any sequence of numbers that may be modeled by a mathematical function. A sequence is an ordered list of numbers such as 1‚ 2‚ 3‚ 4. A pattern can be found in a sequence‚ but a sequence doesn’t always necessarily have a pattern. For some patterns‚ you can even find a rule that fits them. There are two types of rules: recursive and explicit‚ and both rules can be used to find
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but have a more geometric flavor. Write about how you can physically place the blocks. You may assume basic facts about geometric sums and series. Let r be any real number and let n be a non-negative integer. The sum 1 + r + r2 + · · · + rn (1) is a geometric sum and the infinite series 1 + r + r2 + · · · + rn + · · · (2) is a geometric series. Suppose further that r = 1. Then the geometric sum (1) can be computed by the formula 1 − rn+1 . 1 + r + r2 + · · · + rn = 1−r This fact
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general formula for area‚ we can evaluate the area for the first five iterations of the Classic Koch Snowflake as being 0.5773502693‚ 0.6415002993‚ 0.6700114237‚ 0.6826830345‚ 0.6883148616 respectively. We can treat the area formula as a geometric series‚ where r = (4/9) and since (4/9)<1‚ the area for the final snowflake converges to 0.6928203232. The Variation Koch Snowflake starts with the same equilateral triangle as the Classic Koch snowflake. This means finding the area and the perimeter of
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if the first term is 10 and the last term is 781‚250? (1 point) =8 (1-390625)/(1-5) =781‚248 For problems 5 8‚ determine whether the problem should be solved using the formula for an arithmetic sequence‚ arithmetic series‚ geometric sequence‚ or geometric series. Explain your answer in complete sentences. You do not need to solve. 5. Jackie deposited $5 into a checking account in February. For each month following‚ the deposit amount was doubled. How much money was deposited in the checking
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Questions from Questionbank Topic 1. Sequences and Series‚ Exponentials and The Binomial Theorem 1. Find the sum of the arithmetic series 17 + 27 + 37 +...+ 417. 2. Find the coefficient of x5 in the expansion of (3x – 2)8. 3. An arithmetic series has five terms. The first term is 2 and the last term is 32. Find the sum of the series. 4. Find the coefficient of a3b4 in the expansion of (5a + b)7. 5. Solve the equation 43x–1 = 1.5625 × 10–2. 6. In an arithmetic sequence‚
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end. This stand-alone image readies our mind for the possibilities ahead. Graham forces us to take a breath before descending the staircase and viewing the other chapters in his story. After this we find another tale from New Orleans‚ this time a series. A man in a wheelchair‚ struggling to navigate whilst time and space continues on up above him. The juxtaposition of the man with such limited independence and mobility with the power and unpredictability of the ominous storm clouds above show us
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2 (b) Factorise 3x 2 + x – 2. 2 (c) Simplify 2 1 . − n n +1 2 (d) Solve 4 x − 3 = 7. 2 (e) Expand and simplify ( 3 −1 2 3 + 5 . )( ) 2 (f) Find the sum of the first 21 terms of the arithmetic series 3 + 7 + 11 + ··· . 2 – 3 – Marks Question 2 (12 marks) Use the Question 2 Writing Booklet. (a) Differentiate with respect to x : (i) (ii) (iii) ( x 2 + 3) 9 x 2 loge x sin x . x+4 2 2 2 (b) Let M be the midpoint of (–1
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Question 5 - 10 marks (Equity Options) It is January 2nd‚ 2014 and Google Inc. (GOOG) stock is currently trading on the Nasdaq at a price of $1‚105.00 US dollars. Using the information provided below‚ please answer the following questions: (Note: ’Last’ means the last traded price of the put or call option. Use this number for your calculations). Call options: Put options: a) Based on the current stock price‚ which one of the two options is in the money? by how much? (1 marks) b)
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(mn + 1) / 4 (c) (mn + 1) / 2 (d) (mn -1) / 2 11. The first and the last terms of an AP are 107 and 253. If there are five term in this sequence‚ find the sum of sequence. (a) 1080 (b) 720 (c) 900 (d) 620 12. What will be the sum to n terms of the series 8 + 88 + 888 + …? (a) 8(10 n 9n) 81 (b) 8(10 n 1 10 9n) 81 (c) 8(10n-1 – 10) (d) None of these 13. After striking the floor‚ a rubber ball rebounds to 4/5 th of the height from which it has fallen.
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James’s estimate being 35 per cent. About 98 per cent of the rest were of British or Irish origin. The immigration rate from the United Kingdom was exceptionally high between 1910 and 1914. ’Simpson’ - ’the man with the donkey’ was John Simpson Kirkpatrick‚ a recent Geordie emigrant. ’Rule Britannia’‚ ’Soldiers of the Queen’ and ’Sons of the Sea’ were sung at recruiting offices in Adelaide and Sydney‚ Wellington and Christchurch‚ as loudly as in Birmingham or Glasgow. In 1914 and 1915 there was
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