Growing Patterns Math Example 1

Follow the full solution, then compare it with the other examples linked below.

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: \(a_n = 3 + (n-1) \times 4\).

About Growing Patterns

A growing pattern is a sequence where each term increases by following a consistent rule, such as adding the same number each time (2, 5, 8, 11, ...) or multiplying by a constant factor (3, 6, 12, 24, ...). Recognizing the rule lets you predict any term in the sequence.

Learn more about Growing Patterns →

More Growing Patterns Examples

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 1

Example 3 easy

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

Example 4 medium

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

Example 5 medium

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

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