Practice Growing Patterns in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
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.
Imagine stacking blocks in a staircase—each step is one block taller than the last. The pattern grows by a rule: block per step. If the rule is , the staircase grows faster.
Showing a random 20 of 50 problems.
Example 1
mediumA geometric pattern starts . Find the 7th term.
Example 2
mediumFind the 7th term of using the rule.
Example 3
easyDescribe the rule for .
Example 4
easyWhat is the 4th term of ?
Example 5
mediumFind the 12th term of .
Example 6
hardThe sum of the first positive integers is given by . Use it to compute .
Example 7
mediumA pattern goes . Which term equals ?
Example 8
hardFind the 25th term of .
Example 9
mediumWhich term of equals 43?
Example 10
mediumTriangular numbers: . Find the 8th term.
Example 11
easyFind the next term: (square numbers).
Example 12
hardA pattern's 5th term is and 9th term is . Find the common difference.
Example 13
easyWhat is the rule for ?
Example 14
easyFind the next term: .
Example 15
mediumWhat kind of pattern is ?
Example 16
easyA pattern starts: 3, 7, 11, 15, ... Find the next two terms and the rule.
Example 17
mediumWhat is the rule connecting term number and value for ?
Example 18
mediumA figure pattern uses tiles. How many tiles in figure 10?
Example 19
mediumA pattern has and decreases by each step. Find .
Example 20
hardFind the missing term: .