Math 140 Exam 5 Sample - Sequences, Series, and Expansion, Exams of Algebra

Download Math 140 Exam 5 Sample - Sequences, Series, and Expansion and more Exams Algebra in PDF only on Docsity! Sample Exam for Exam 5 Math 140 Section C Instructions: This is a sample exam for Exam 5 which is on Apr. 29. 2009. All problems in Exam 5 will be similar to the problems in this sample exam. Please notice that the number of problems in Exam 5 may be different from it is in this sample exam. 1. Find the general term, an, for each of the following sequences. (a) 1 · 2, 2 · 3, 3 · 4, 4 · 5, 5 · 6, · · · (b) −2, 6,−18, 54, · · · 2. Let an = 5 + (−2)n+1 2n . Find a3 and a20. 3. Find and evaluate each of the following sums. (a) 8∑ k=1 k k + 1 (b) 5∑ k=2 k2 − 3k + 1 1 4. Write the sigma notation for each of the following. (a) 4 − 9 + 16 − 25 + · · · (b) 1 2 + 1 6 + 1 12 + 1 20 + 1 30 + 1 42 5. Find each of the following for the arithmetic sequence : 32 , 9 4 , 3, 15 4 , · · · (a) The common difference, d. (b) The general term, an. (c) The partial sum, S 26. 6. Find each of the following for the geometric sequence with a1 = 4 and a2 = 4 √ 2. (a) The common ratio, r. (b) The general term, an. (c) The partial sum, S 10. 2