Consider the arithmetic series 2 + 5 + 8 +.... (a) Find an expression for Sn‚ the sum of the first n terms. (b) Find the value of n for which Sn = 1365. (Total 6 marks) 11. Find the sum to infinity of the geometric series (Total 3 marks) 12. The first and fourth terms of a geometric series are 18 and respectively. Find (a) the sum of the first n terms of the series; (4) (b) the sum to infinity of the series. (2) (Total 6 marks) 13. Find the coefficient of x7 in the expansion
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Solutions 1. Mixture Problems: 2. Value of the Original Fraction: 3. Value of Numerical Coefficient: 4. Geometric Series: 5. Simplify: 6. Mean Proportion: 7. Value of x to form a geometric progression: 8. Value of x: 9. Work Problem: 10. Value of the original number: 11. Sum of the roots: A = 5‚ B = -10‚ C = 2 12. Work Problem: 13. Value of m: 14. Age Problem: Subject Past
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Nike‚ Inc.: Cost of Capital Case 14 A Case Brief Submitted to Submitted by In Partial Fulfillment of the Requirements for Date Submitted September 28‚ 2011 Summary This case highlights Kimi Ford‚ a portfolio manager with NorthPoint Group‚ a mutual-fund management firm. She managed the NorthPoint Large-Cap Fund‚ and in July of 2001‚ was looking at the possibility of taking a position in Nike for her fund. Nike stock had declined significantly over the previous year‚ and it appeared
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Topics Topic 1—Algebra 1.1 The nth term of an arithmetic sequence The sum of n terms of an arithmetic sequence The nth term of a geometric sequence un = u1 + (n − 1)d S n= n n (2u1 + (n − 1)d ) = (u1 + un ) 2 2 un = u1r n −1 The sum of n terms of a u1 (r n − 1) u (1 − r n ) ‚ r ≠1 = = 1 Sn finite geometric sequence r −1 1− r The sum of an infinite geometric sequence 1.2 Exponents and logarithms Laws of logarithms S∞ = u1 ‚ r 0 − cos ∫ sin x dx = x + C = ∫ cos x dx sin x + C ∫e
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In this week’s assignment I will attempt complete exercises 35 and 37 in the “Real World Applications” section on page 280 of Mathematics in Our World. For each exercise‚ specify whether it involves an arithmetic sequence or a geometric sequence and use the proper formulas where applicable. I will try to format my math work as shown in the “week one assignment guide” provided to us and try to be concise in my reasoning. Exercise 35: A person hired to build a CB Radio tower. The firm charges
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the third term of a geometric progression is 20 and the sum of its first three terms is 26. Find the progression. (a) 2‚ 6‚ 18… (b) 18‚ 6‚ 2‚… (c) Both of these (d) Cannot be determined 4. The sum of 5 numbers in AP is 30 and the sum of their squares is 220. Which of the following is the third term? (a) 5 (b) 6 (c) 8 (d) 9 5. Find the general term of the GP with the third term 1 and the seventh term 8. (a) (23/4)n-3 (b) (23/2)n-3 (c) (23/4)3-n (d) None of these Four geometric means are inserted
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form an edge. I.e – Each straight line - Becomes this - Hence now for everyone 1 line‚ 4 new ones are formed. Hence we can say that there is geometric progression‚ by the factor 4. Hence‚ the formula for the number of sides is Nn = 3(4)n Length of Side The length of the next side is one-third the previous length. This is once again geometric progression. Therefore‚ the equation for the nthterm is: Ln = Perimeter The perimeter of any shape = Length of each side x Number of sides
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cost for the first month when the baby was born was RM22. What a) were the expenses for the 10th month and the 15th month after the baby was born? (4m) b) were the total expenses for the first two years? (3m) 3. Three successive terms of a geometric sequence are x – 6 ‚ x and 9 + 2x. All the terms of the sequence are positive. a) Find x. (2m) b) If x is the fifth term‚ find the first term of the sequence. (2m) 4. The monthly maintenance cost of a car increases by 2% from the previous month’s
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Thomas Malthus Principles of Population Today‚ there is both agreement and disagreement of Thomas Malthus’ essay on the principles of population. Malthus stated that population grows exponentially or at “geometric rate” and food production grows at arithmetic rate‚ or linearly. Geometric rate grows in a series of numbers (2‚4‚8‚16‚32…etc.)‚ which shows that children will grow up and each have their own children‚ and those children will have their own children. Eventually the base numbers of children
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Susan Dellinger: Psycho-Geometrics I love great public speakers. I’ve seen some great ones in my life. They captivate the audience‚ entertain‚ educate‚ even make you laugh. The most important part is that they make it look effortless and natural. Susan Dellinger‚ the speaker for the video‚ "Psycho-Geometrics" is one of them. Her presentation was incredibly entertaining‚ interesting‚ and funny. But the focal point was definitely Ms. Dellinger herself. The level of excitement in her voice was great
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