Growing Patterns Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Growing Patterns.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A pattern where each term changes by a consistent rule, such as adding the same number each time.

Imagine stacking blocks in a staircase—each step is one block taller than the last. The pattern grows by a rule: +1 block per step. If the rule is +3, the staircase grows faster.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Growing patterns change by a rule—finding the rule lets you predict any term in the sequence.

Common stuck point: Distinguishing between the pattern rule (what changes) and the starting value (where it begins).

Sense of Study hint: Write the differences between consecutive terms below each gap to find the rule that generates the pattern.

Worked Examples

Example 1

easy
A pattern starts: 3, 7, 11, 15, ... Find the next two terms and the rule.

Solution

  1. 1
    Find the common difference: \(7-3=4\), \(11-7=4\), \(15-11=4\).
  2. 2
    The rule is: add 4 each time.
  3. 3
    Next term: \(15 + 4 = 19\).
  4. 4
    Term after: \(19 + 4 = 23\).

Answer

19, 23 (rule: add 4)
This is an arithmetic sequence with first term \(a_1 = 3\) and common difference \(d = 4\). Formula: \(a_n = 3 + (n-1) \times 4\).

Example 2

medium
The first term of a pattern is 5 and it grows by 6 each time. Using \(a_n = a_1 + (n-1)d\), find the 10th term.

Example 3

medium
Find the 10th term of the pattern: 3, 7, 11, 15, ...

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A sequence goes: 2, 9, 16, 23, ... What are the next two terms?

Example 2

medium
A pattern has \(a_1 = 10\) and \(d = 5\). Find the 8th term using \(a_n = a_1 + (n-1)d\).
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Background Knowledge

These ideas may be useful before you work through the harder examples.

simple patternsaddition