A repeating pattern is a sequence where a specific block of numbers, called the 'core', repeats over and over.
What is the 'core' of a repeating pattern?
The core is the shortest part of the sequence that repeats. For the pattern \(1, 2, 3, 1, 2, 3, ...\), the core is \(1, 2, 3\).
Find the core of the pattern: \(8, 4, 2, 8, 4, 2, 8, ...\)
The core of the pattern is \(8, 4, 2\).
Find the core of the pattern: \(A, B, B, A, B, B, A, ...\)
The core of the pattern is \(A, B, B\). Repeating patterns can use letters or shapes too!
What are the next three numbers in the pattern \(9, 0, 1, 9, 0, 1, ...\)?
The next three numbers are \(9, 0, 1\). The core \(9, 0, 1\) repeats.
Consider the pattern \(5, 1, 5, 1, ...\). What will the \(7\)th term be?
The \(7\)th term will be \(5\). The pattern is \(5, 1, 5, 1, 5, 1, 5, ...\). Odd-numbered positions are \(5\).
The core of a repeating pattern is \(4, 3, 2, 1\). What is the \(10\)th term in the sequence?
The \(10\)th term is \(3\). The sequence is \(4, 3, 2, 1, 4, 3, 2, 1, 4, 3, ...\). The core has \(4\) numbers. The \(10\)th term is the same as the \(2\)nd term in the core.
Find the missing number in this repeating pattern: \(6, 7, 8, 6, \_\_, 8, 6, 7, 8\).
The missing number is \(7\). The core of the pattern is \(6, 7, 8\).
Is the pattern \(1, 1, 2, 1, 1, 2, ...\) a repeating pattern?
Yes. The core of the pattern is \(1, 1, 2\).
A traffic light cycles through red, yellow, and green. If it just turned red, what color will it be after \(5\) more changes?
It will be green. The pattern of changes is: Yellow (1st change), Green (2nd), Red (3rd), Yellow (4th), and Green (5th).
