Patterns and Sequences

Do you like reading mystery books and trying to solve the crime before the detective does? Do you love looking for hidden clues that point to what will happen next? If you do, you are already a master of pattern recognition.

In the universe of math, patterns are the ultimate clues. When a group of numbers or shapes follows a specific, repeating rule, we call it a sequence. Once your brain figures out the secret rule behind a sequence, you gain a superpower: the ability to predict the future of that number line forever!

Cracking the Code: Simple Sequences

Every number sequence has a hidden operation rule that controls how it grows or shrinks. Let’s look at a few basic types and see how they operate:

• The Addition Ladder: Look at this string of numbers: 3, 7, 11, 15, 19... How do we get from 3 to 7? We add 4! How do we get from 7 to 11? We add 4 again! The secret rule of this sequence is +4. Now that you know the rule, you can find the next number easily: 19 + 4 = 23.
• The Subtraction Slide: Sequences can also shrink! Check out this line: 50, 45, 40, 35, 30... The numbers are dropping by the exact same amount every single time. The secret rule here is -5, meaning the next number waiting in line must be 25.
• The Geometric Explosion: Sometimes, numbers don't just walk up a ladder—they sprint ahead by multiplying! Look at this sequence: 2, 4, 8, 16, 32... Instead of adding, we are multiplying by 2 (doubling the number) every time. The next giant step would be 32 x 2 = 64!

Why Patterns Rule the World

Mathematicians and scientists spend their entire lives hunting down patterns because they let us solve massive global problems. Weather forecasters look at data patterns to predict if a massive storm will form next week, saving thousands of lives.

Cybersecurity experts use pattern math to crack encrypted computer codes and protect bank accounts from internet hackers, while astronomers track the movement patterns of stars to calculate the exact second a solar eclipse will pass over our town.

Your Turn: Become a Sequence Detective!

Grab a pencil and try to find the secret rule and the missing number for these three mystery code sequences:

• Code 1: 10, 20, 30, 40, 50, [__]
• Code 2: 1, 3, 9, 27, 81, [__]
• Code 3: 100, 90, 80, 70, 60, [__]

(Answers: Code 1 increases by +10, so the missing number is 60. Code 2 multiplies by 3, so the missing number is 243! Code 3 subtracts 10, so the missing number is 50.)