Linear Sequences
What is the next term in the sequence 3, 7, 11, 15, …?
19
What is the next term in the sequence 1, 4, 9, 16, …?
25 (squares of consecutive integers)
Define an arithmetic sequence.
A sequence in which the difference between consecutive terms is constant.
Define a geometric sequence.
A sequence in which each term is found by multiplying the previous term by a constant, called the common ratio.
ChatGPT is thinking of two numbers. It adds them together to get 12, then multiplies them to get 35. What are the two numbers?
5 and 7
What is the next term in the sequence 12, 15, 18, 21, …?
24
What is the next term in the sequence 5, 10, 20, 40, …?
80 (each term is multiplied by 2)
What is the common difference in the sequence 10, 15, 20, 25, …?
5
What is the common ratio in the sequence 3, 6, 12, 24, …?
2
Cal divides a chocolate bar evenly among four friends, but one piece mysteriously disappears! Each friend gets a whole number of pieces, and the total number of pieces in the bar was between 20 and 30. How many pieces were there originally, and how many did each friend get?
24 and each gets 6
What is the next term in the sequence -5, 0, 5, 10, …?
15
What is the next term in the sequence 2, 6, 18, 54, …?
162 (each term is multiplied by 3)
If the first term of an arithmetic sequence is 2 and the common difference is 4, what is the 5th term?
18
If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 4th term?
135
wangGPT is pushing his car along a road when he suddenly stops, realising he's at a hotel. Why does he stop?
He’s playing Monopoly and landed on a hotel.
What is the next term in the sequence 20, 16, 12, 8, …?
4
What is the next term in the sequence 3, 9, 27, 81, …?
243 (each term is multiplied by 3)
Given the sequence 7, 12, 17, 22, …, what is the 10th term?
52
Given the sequence 2, 10, 50, 250, …, what is the 5th term?
1250
Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?
R
What is the next term in the sequence 50, 41, 32, 23, …?
14
What is the next term in the sequence 1, 1, 2, 3, 5, …?
8 (Fibonacci sequence)
If the first term of an arithmetic sequence is 10 and the common difference is -3.2, what is the 5th term?
-2.8
Given the sequence 2, 10, 50, 250, …, what is the 6th term?
6,250
I speak without a mouth and hear without ears. I have no body, but I come alive with wind. What am I?
Echo