EXAM 1 REVIEW (Actual Exam will consist of 14 problems. You may use only regular scientific calculator) 1. Knowing, that 1 + 2 + 3 + ... + n = + find 1 1+ +2+3+ ..+ 165 = 2. Knowing, that the formula for the Pentagonal numbers is Pn = find the 31 st 2 Pentagonal number. 3. For each sequence show your work: I. Determine if it is an arithmetic sequence, geometric sequence, or neither. II. For the arithmetic sequence determine the common difference and the next term, for the geometric sequence determine the common ratio and the next term. III. For the sequences that are neither, use the method of Successive Differences to find the next term. a) 6, 20, 50, 102, 182, 296, ... b) 256, 128,64,32, 16, ... c) 1, 8, 15, 22, 29, 36, ... d) 3, 12, 48, 192, 768,... 4. When 6 gallons of gasoline are put into a car's tank, the indicator goes from = of a tank to What is the total capacity of the gasoline tank? 5. Let U = {a, b, c, d, e, f, g, h}, A = {a, b, c, d}, B = {e, f, g, h}, and C = {e, g}. Perform the indicated operations, and designate each answer using the listing method. a) COB; b)AUB; c) C'; d) B -(Anc') 6. Let A = {b, l, u, e} and B = {2, 3}. a) Find the Cartesian Product A X B; b) Write the formula, then use it to find n(A x B) 7. If A and B are sets and n(A) = 9, n(B) = 21, and n(A U B)=24, find n(An B). 8. Robert works in the Home Economics 58 use microwave ovens Department of Electric Utility. He interviewed 63 use electric ranges 140 people in suburban shopping center to 58 use gas ranges find out some of their cooking habits. He 19 use microwave ovens and electric ranges 17 use microwave ovens and gas ranges obtained the following results: 4 use both electric and gas ranges 1 use all three 2 cook only with solar energy, Construct a Venn Diagram, then answer how many households use (a) only one appliance, (b) exactly two appliances, (c) at least two appliances. 9. Negate the following statements: a) Some whole numbers are integers. b) All rational numbers are real numbers.10. Explain the difference between the following statements: All flowers in the bouguet are not yellow. Not all flowers in the bouguet are yellow. 11. Let p represent the statement "7This dessert is delicious\" and let represent the statement: "The dessert is expensive". Translate each symbolic compound statement into words: a)pA ~q b)p-q 12. Let p represent the statement "Ana is a doctor\