1) Given the sequence of numbers: {-3,1,5,9,13}

a) What kind of set is the sequence? 

b) What kind of progression is it?

c) What is the common difference/ratio? 

d) What are the extremes of the progression? e) What are the means of the progression?

 

2) Given the sequence of numbers: {-3,9,-27,...}

a) What kind of set is the sequence? 

b) What kind of progression is it? 

c) What is the common difference/ratio? 

d) What are the extremes of the progression? 

e) What is the sum of the 10th to 30th terms of the progression? 

f) If the common ratio/difference was changed to -0.5, what is the total sum of the progression?

 

3) Given the extremes: -3 and 16

a) Insert 15 arithmetic means between them. 

b) Insert 5 arithmetic means between them, then get the sum of the first 4 terms. 

c) Insert 6 Geometric means between them. (Use 5 decimal places for r)

 

4) A survey for 500 children is conducted in a town. The results show that approximately 53 % liked eating candies, 49% liked eating fruits and 55% liked eating rice. In addition, 5% liked eating candies and fruits but not rice, 8% liked eating rice and fruits but not candies, and 10% liked eating candies and rice but not fruits. 6% did not like eating candies, fruits, or rice.

 a) How many children like eating all food (candies, fruits, and rice)? 

b) How many children like eating candies only? 

c) How many children like eating fruits only? 

d) How many children like eating only one type of the foods listed? 

e) Find the number of children who like eating at least two of the given foods.

 *** Draw the Venn diagram illustrating the problem. 

 

5) Given that a varies directly as the product of b and c and inversely as the square of x, answer the following questions.

 

 a) Write the notation showing the variation described. 

b) What is the type of variation described? 

c) If a = 3, b=100, c=-7, x=-16, what is k? 

d) Determine the value of a if b=33, c=-49, and x=-4. 

e) Determine the value of a if b=-16, c=300, and x=-25. 

f) If a = 52, b=36, c=-0.5, x=-35, what is k?