Sequences, Series & Patterns
Happy New Year! Now that 2019 is here, let’s have some fun solving this collection of problems that all involve the number 2019.
What is the greatest prime factor of 2019?
The factors of 2019 are 1, 3, 673, 2019. The prime factors of 2019 are 3 and 673, the greatest being 673.
The Land O’ Lakes High School auditorium has exactly 26 rows of seats. The rows are labeled, in order, from the front of the auditorium to the back from A through Z. There are 8 seats in the row A. Each row after the first row has two more seats than the previous row. There are 10 seats in row B, 12 seats in row C and so on. How many seats are there in row Z?
In the video arcade game Asteroid Blaster there are a total of five rounds on the first level. During each round, asteroids appear on the screen and players must blast as many as possible before time expires. To advance to the next round, a player must destroy all the asteroids in the current round. This becomes more difficult to accomplish because the number of asteroids increases with each round. Rounds 1, 2 and 3 each have 1, 8 and 27 asteroids, respectively. If this pattern continues, how many asteroids will there be to destroy in Round 4?
What is the 20th term of the arithmetic sequence 13, 19, 25, 31, ...?
The common difference is 19 – 13 = 6. Now that we know that we can find the 20th term by 13 + 6(20 – 1). Thus, the 20th term is 127.
What is the sum of A and B in the arithmetic sequence 7, 15, 23, A, 39, B, ...?