Sequences, Series & Patterns
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, ...?
This Saturday’s date, 02-10-18, forms an arithmetic sequence since 2 + 8 = 10 and 10 + 8 = 18. In honor of this occurrence, try your hand at solving these problems involving sequences and patterns.
What is the tenth term of the sequence −50, −49, −47, −44, −40, …?