In a pattern that which repeats is called the core. Every element, number, symbol, or shape, is called a term.
535535535
In the above example 535 is our core and 5 is the fourth term and 3 is the fifth.
The first thing you need to do when solving patterns is to identify the core. Look for repeating elements and make sure they repeat in order. It sometimes helps to say them out loud.
To determine higher terms, count by the number of terms in the core.
In our example 535, we could count by threes to predict later terms, so our 24th term and any term that is a multiple of 3 will be 5. One less than a multiple of 3 would be 3 and one more than a multiple of 3 would be 5.
For more complex patterns, make a table of term numbers compared to what number is found at the term position. Determine if the pattern is increasing or decreasing and what it is increasing by.
Consider the following pattern:
4,7,10,13,16
Each term increases by a factor of 3 but is one more than the multiples of three. This creates an equation that governs the pattern.
y = 3x + 1
Now Consider this pattern:
3,7,11,15, 19
This time the pattern increases by 4 but is one less than multiples of 4. Our governing equation is now.
y = 4x - 1
These equations can be graphed and the line of best fit used to predict future terms.
