Math IP 5 Essay Example | Topics and Well Written Essays - 750 words

Math IP 5 - Essay Example Answer: 3 Show work in this space. 27 9 =3 9 3 = 3 3 1 = 3 b) Using the formula for the nth term of a geometric sequence, what is the 10th term Answer: 19683 Show work in this space. a10 = a1 rn-1 a10 = (1) (3) 10-1 = (1) (19683) = 19683 c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms Answer: 29524 Show work in this space. Sn = a1 (1- rn) / 1-r = 1 (1-310) / 1-3 = 1 (1-59049) / -2 = -59048 / -2 = 29524 3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27 to find the following: a) What is r, the ratio between 2 consecutive terms Answer: 1/3 Show work in this space. 1/27 1/9 = 1/3 1/9 1/3 = 1/3 1/3 1 = 1/3 b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms Carry all calculations to 6 decimals on all assignments. Answer: 1.499976 Show work in this space. Sn = a1 (1- rn) / 1-r = 1 (1-(1/3)10) / 1-1/3 = 1 (1- 1.693508-5) / 2/3 = 1. 49976 c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms Carry all calculations to 6 decimals on all assignments. Answer: 1.499998 Show work in this space. Sn = a1 (1- rn) / 1-r = 1 (1-1/312) 1-1/3 = 1 (1-1.881676-6) 1-2/3 = 1.499998 d) What observation can make about the successive partial sums of this series In particular, what number does it appear that the sum will always be smaller than Answer: When plotted in a graph, it is expected that the partial sum of the series is a graph which grows flatter over time. This is because the partial sums grow slower over each value. The sum will always be smaller than 3....He rushed over and pulled a young lady out of the flaming truck. Farmer Crane came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Crane insisted on giving the man an award for his heroism. So, the salesman said, "If you insist, I do not want much. Get your checkerboard and place one grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat." As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved. c) Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman Please provide the answer in either scientific notation, or calculate and show all 20 digits.