Practice Exercises.pdf

Practice Exercises Arithmetic Sequence and Series 1. 45th term of an arithmetic sequence having a = 3 and d = 8 is: 2. Find the last term of an arithmetic sequence whose a = 1, d = 2 and n = 1001. 3. Find the sum of the positive terms of the arithmetic sequence 85, 78, 71, … 1...

Practice Exercises Arithmetic Sequence and Series 1. 45th term of an arithmetic sequence having a = 3 and d = 8 is: 2. Find the last term of an arithmetic sequence whose a = 1, d = 2 and n = 1001. 3. Find the sum of the positive terms of the arithmetic sequence 85, 78, 71, … 1 4. A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd, and so on, how many seats are there in all? Assume the pattern continues. Geometric Sequence and Series 1. Find the 8th term of the sequence -1, -3, -9, -27,... 2. Find the common ratio, r, in the sequence 31104, 5184, 864, ___, ___, ___,. 3. The common ratio of a geometric sequence is 3 and the sum of the first five terms is 968. Find the value of the first term. 4. A population of ants is growing at a rate of 8% a year. If there are 160 ants in the initial population, find the number of ants after 6 years. Harmonic and Fibonacci Sequence 1. Find out the next terms in the given Fibonacci sequence 2, 1, 3, 4, 7, ___, ___, ___. 2. What is the value of the 21st term of the harmonic progression: 1/5, 1/9, 1/13, 1/14.....? Sets and Set Operations with Problem-Solving 1. Let U = {{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; A = {1, 3, 5, 7}, B = {2, 4, 6, 8} and C = {3, 6, 9, 0}. Find the following: a) A È B b) B Ç C c) A’ Ç B’ d) (A È B)’ 2. A group of students were asked whether they are like basketball, softball, or both. If 456 like basketball, 384 like softball, and 252 like both games, how many students were there? 3. A survey of 100 fourth year high school students revealed that 42 like mathematics, 62 like Filipino, 44 like History, 22 like both Math and History, 25 like both Math and Filipino, 17 like Filipino and History, and 10 like all the three subjects. How many like Math only? Filipino only? History only? How many did not like any of the three subjects?  Polya’s Problem-Solving Strategy 1. A new burger restaurant offers two kinds of buns, three kinds of meats, and two types of condiments. How many different burger combinations are possible that have one type of bun, one type of meat, and one condiment type? 2. Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number? 3. Nathaly deposited Php 12,500 in her bank account where it will earn 4% interest. How much interest will Nathaly earn in 5 years? Inductive and Deductive Reasoning Identify the reasoning process, inductive or deductive 1. Every President of the United States has been male. The next two Presidents of the United States will be men. 2. The World Cup is held every four years. The last time it was held was in 2006. The next World Cup will be in 2010. 3. What goes up must come down. It went up. It will come down. 4. The Sun has risen in the east every day of Tim’s life. It will rise in the east tomorrow Statements and Quantifiers Translate each statement into symbolic notation. Let 𝑃 represent "I like Pepsi" and let 𝐶 represent "I like Coke." a. I like Pepsi or I like Coke. b. I like Pepsi and I like Coke. c. I do not like Pepsi. d. It is not the case that I like Pepsi or Coke. e. I like Pepsi and I do not like Coke.  Answer Key Arithmetic Sequence and Series 1. 355 2. 2001 3. S13=559 4. S32=2816 Geometric Sequence and Series 1. -2187 2. 6 3. 16 4. 254 Harmonic and Fibonacci Sequence 1. 11, 18, 29 2. 1/85 Sets and Set Operations with Problem-Solving 1. Let U = {{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; A = {1, 3, 5, 7}, B = {2, 4, 6, 8} and C = {3, 6, 9, 0}. Find the following: a) A È B Answer: A È B = {1, 2, 3, 4, 5, 6, 7, 8} b) B Ç C Answer: B Ç C = {6} c) A’ Ç B’ Answer: A’ Ç B’ = {0, 9} d) (A È B)’ Answer: (A È B)’ = {0, 9} 2. Answer: 588 3. Answer: Math only = 5 Filipino only = 30 History only = 15 6 didn’t like any of the three subjects Polya’s Problem-Solving Strategy 1. 12 combinations 2. 9 3. Php 2,500 Inductive and Deductive Reasoning Identify the reasoning process, inductive or deductive 1. Inductive 2. Deductive 3. Deductive 4. Inductive  Statements and Quantifiers Translate each statement into symbolic notation. Let 𝑃 represent "I like Pepsi" and let 𝐶 represent "I like Coke." a. I like Pepsi or I like Coke. b. I like Pepsi and I like Coke. c. I do not like Pepsi. d. It is not the case that I like Pepsi or Coke. e. I like Pepsi and I do not like Coke. Answer: a. 𝑃∨𝐶 b. 𝑃∧𝐶P c. ∼𝑃 d. ∼(𝑃∨𝐶) e. 𝑃∧∼𝐶