# answer question 1 to 8 only. Topic: Arithmetic and geometric series. 1. Determine the number of terms and the sum of the sequence: 5‚ 11‚ 17‚ … ‚ 83. (14‚ 616) 2. The fourth term and the 8th term of an arithmetic sequence are 16 and 32 respectively. Find: a) Common difference (4) b) the sum of the first 20 terms of this
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2013 JC1 December Holiday Assignment JJC 2012 H2 Mathematics Promotional Examination 1 −2 Expand ( k + y ) up to and including the term in y 2 ‚ where k is a non-zero constant. State the range of values of y for which the expansion is valid. [4] In the expansion of ( k + x + 2 x 2 ) −2 in ascending powers of x‚ the coefficient of x 2 is zero. Find the value of k. 2 The curve C has equation y = [3] 2x + a ‚ where a is a positive constant. By rewriting the equation x−3 B ‚ where A and B are
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monthly‚ etc. These need to be converted to annual rate of returns Arithmetic & Geometric Rates of Return If we invest $100 for 2 years and at the end of 2 years we receive $120 * Arithmetic (Mutual funds often quote their past rates of return using this method) * $20 / 2 years = 10% * Geometric (This is correct because it allows for compounding) * TVM = 9.5445% Arithmetic Mean & Geometric Mean Return Year | Return (%) | 1990 | 17 | 1991 | 8 | 1992 | 2 |
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Geometric and Arithmetic Sequences to Questions 35 & 37 MAT-126: Survey of Mathematical Methods(ACO1141A) October 11‚ 2011 As one observes an arithmetic sequence‚ it is imperative to use inductive and deductive reasoning to use the right mathematical approach of geometric or arithmetic sequence to solve the equation in the most pragmatic way. Most times both inductive and deductive reasoning is used on an equation or variable to come up with the most direct approach to an answer
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sides | A 4-sided figure with 2 pairs of parallel sides and all sides the same length | A circle is also a plane figure. A circle is a plane figure in which all the points are the same distance from a point called the center. | You can use geometric shapes to help describe real-world objects. | name the shapeThe toy is a TRIANGLE.It is a ploygon with 3 sides. | | name the shapeThe keyboard is a RECTANGLE.It is a 4-sided figure with 4 angles and opposite sides parallel and the same length
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Rock Harmony (Andy Goldsworthy: “Rock Creation”) Richard Lipoczi Art 100 Jennifer Monroe 04/25/2013 Andy Goldsworthy is a British naturalist artist‚ mostly sculptor and photographer‚ creating in the twentieth and twenty-first centuries. He is still alive in these days. All his works draw on their themes from the nature: he uses only natural materials in their original environments to his works. He expresses his thoughts through transforming the natural matters to certain kinds of
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meters)‚ and carpet price per square meter. 4. Compute and print the number of minutes in a year. 5. Given a positive number‚ print its square and square root. 6. The arithmetic mean of two numbers is the result of dividing their some by 2. The geometric mean of two numbers is the square root of their product. The harmonic mean of two numbers is the arithmetic mean of their reciprocals. Write a program that takes two floating-point numbers as inputs and displays these three means. 7. Write a
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A population of 80 longhorn cattle was introduced onto an island on 1 October 1960. There was no subsequent migration of longhorn cattle to or from the island. Let Pn denote the size of the longhorn cattle population on the island on 1 October n years after 1960. (a) In this part assume that‚ for each integer n ≥ 0‚ the number of births and deaths in the year beginning 1 October n years after 1960 are 1.52Pn and 1.24Pn‚ respectively. (i) Find a recurrence system satisfied by Pn. (ii) State
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Treasury Yield forecast. We used this rate because WACC is used for long-term projects and therefore‚ the longest treasury rate should also be used. b. The market risk premium is the geometric mean of 5.9%. The geometric mean was used‚ as it is a common measure for measuring the results of a portfolio. The geometric mean uses percentages and it is therefore much more accurate than the standard arithmetic mean. c. The Beta that was used to gain a return on equity equivalent to 10.5% was 0.8‚ the
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………………………………………….. (b) ………………………………………….. (Total 4 marks) 2. The population of Bangor is growing each year. At the end of 1996‚ the population was 40 000. At the end of 1998‚ the population was 44 100. Assuming that these annual figures follow a geometric progression‚ calculate (a) the population of Bangor at the end of 1997; (b) the population of Bangor at the end of 1992. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 4 marks) 3. Mr Jones decides to increase
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