Growing Patterns Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumThe 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.
Solution
- 1 Given: \(a_1 = 5\), \(d = 6\), find \(a_{10}\).
- 2 Apply formula: \(a_{10} = 5 + (10-1) \times 6\).
- 3 \(a_{10} = 5 + 9 \times 6 = 5 + 54 = 59\).
- 4 The 10th term is 59.
Answer
59
The arithmetic sequence formula \(a_n = a_1 + (n-1)d\) lets us jump directly to any term without listing them all.
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 3 easyA sequence goes: 2, 9, 16, 23, ... What are the next two terms?
Example 4 mediumA pattern has (a_1 = 10) and (d = 5). Find the 8th term using (a_n = a_1 + (n-1)d).
Example 5 mediumFind the 10th term of the pattern: 3, 7, 11, 15, ...