Growing Patterns Math Example 5

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

Example 5

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

Solution

  1. 1
    Identify the common difference: 7−3=47 - 3 = 4, 11−7=411 - 7 = 4, 15−11=415 - 11 = 4. So d=4d = 4.
  2. 2
    Use the formula an=a1+(n−1)da_n = a_1 + (n - 1)d with a1=3a_1 = 3, d=4d = 4, n=10n = 10.
  3. 3
    Substitute: a10=3+(10−1)×4=3+9×4=3+36=39a_{10} = 3 + (10 - 1) \times 4 = 3 + 9 \times 4 = 3 + 36 = 39.

Answer

3939
A growing pattern with a constant difference is an arithmetic sequence. Using the general term formula avoids having to list every term up to the one you need.

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 1 easy

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

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).

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