Sequences and Patterns

General Sequences

2020 July(C01) Math Question 7

2019 April(B04) Math Question 10

2019 June(72F) Math Question 10

12. The table below gives the total charge to rent a moving truck from each of 2 movers for various numbers of miles. For what number of miles would the total charge for renting a moving truck from Ben's be the same as the total charge for renting a moving truck from Ronnie's? (Note: There is a linear relationship between the number of miles and the total charge for both Ben's and Ronnie's.)

2015 April(73G) Math Question 12

2009 June(67C) Math Question 13

2011 April(67F) Math Question 14

17. The first 5 terms of a sequence are given in the table below. The sequence is defined by setting al = 9 and a„= an _1+ (n — 1)2 for n ?_ 2. What is the sixth term, a6, of this sequence?

2016 December(74H) Math Question 17

2009 June(67C) Math Question 18

2009 June(67C) Math Question 23

24. Observation of a certain bacteria colony has shown that its population of cells doubles every 3 hours. Given that the initial population of cells in this colony is about 8 million, which of the following values, in millions, would be closest to the number of cells in the bacteria colony after 15 hours?

2015 April(73G) Math Question 24

2009 December(68A) Math Question 25

2019 June(72F) Math Question 27

34. The sum of a sequence of consecutive odd numbers, where the smallest term is 1, is always a perfect square. For example, 1 + 3 = 22 and 1 + 3 + 5 + 7 = 42- One of the sequences described above has a- sum of 144. What is the largest odd number in the sequence?

2013 June(71C) Math Question 34

2011 June(69F) Math Question 35

2019 December(C03) Math Question 40

45. Given today is Tuesday, what day of the week was it 200 days ago?

2017 June(74C) Math Question 45

47. The recursive formula for a sequence is given below,
where an is the value of the nth term.
a1 = 10
an= a n-1 + 5
Which of the following equations is an explicit
formula for this sequence?

2019 June(B02) Math Question 47

2019 April(B04) Math Question 47

2012 June(70C) Math Question 48

48. Consider all positive integers that are multiples of 20 and that are less than or equal to 300. What fraction of those integers are multiples of 15 ?

2016 December(74H) Math Question 48

50. The fraction is equivalent to 0.285714. What is the digit in the 1,001st decimal place of 0.285714 ? (Note: The digit in the 4th decimal place of 0.285714 is 7.)

2016 December(74H) Math Question 50

51. A teacher assigns each of her 18 students a different integer from 1 through 18. The teacher forms pairs of study partners by using the rule that the sum of the pair of numbers is a perfect square. Assuming the 9 pairs of students follow this rule, the student assigned which number must be paired with the student assigned the number 1?

2015 June(73C) Math Question 51

53. Suppose that equally spaced dots are marked on each side of a regular polygon, with a dot at each vertex, and that the distance between consecutive dots is the same for all sides. The figure below shows 4 equally spaced dots per side, including a dot at each vertex, for an equilateral triangle. Which of the following expressions represents the number of dots for a regular polygon with n equally spaced dots, including one at each vertex, marked on each of its s sides?

2015 April(73G) Math Question 53

54. A storage facility is currently offering a special rate to customers who sign contracts for 6 months or more. According to this special rate, the first month's rent is $1, and for each month after the first month, customers pay the regular monthly rental rate. The table below shows the storage unit sizes available, the floor dimensions, and the regular monthly rental rate. All the units have the same height. Dania will sign a contract to rent a Size 3 unit for 12 months at the current special rate. The amount Dania will pay for 12 months at the current special rate represents what percent decrease from the regular rental rate for 12 months?

2015 April(73G) Math Question 54

2019 April(B04) Math Question 55

2019 April(Z15) Math Question 56

2019 April(B04) Math Question 57

2012 December(71A) Math Question 58

59. The sum of the first 30 positive integers is 465. Which of the following is the sum of the first 60 positive integers?

2014 April(71H) Math Question 59

60. Mr. Martin wants to plant 7 trees evenly spaced along a straight fence 300 feet long, with 1 of the trees at each end of the fence. About how many feet apart should he plant the trees?

General SequencesSequences and PatternsACT math questions

2020 July(C01) Math Question 7

2019 April(B04) Math Question 10