Growing patterns (Tutorial Only)

Learning Objectives Identify and describe growing patterns in numerical and visual sequences. Determine the rule for a given growing pattern. Predict subsequent terms in a growing pattern using its rule. Represent growing patterns using tables and algebraic expressions. Distinguish between patterns with a constant difference (arithmetic) and those with a constant ratio (simple geometric). Apply pattern rules to solve real-world problems. Ever noticed how things grow in a predictable way, like the number of petals on a flower or the steps in a staircase? 🌸 Let's discover the hidden rules behind these amazing growing patterns! In this lesson, you'll learn to spot, describe, and predict what comes next in sequences that grow. Understanding these patterns will help y...

TermDefinitionExample PatternA sequence of numbers, shapes, or objects that follows a predictable rule or order.The sequence 2, 4, 6, 8, ... is a pattern where each number increases by 2. TermEach individual number, shape, or object in a pattern or sequence.In the pattern 5, 10, 15, 20, ..., '5' is the 1st term, '10' is the 2nd term, and so on. Term Number (Position)The position of a term in a sequence, usually denoted by 'n' (e.g., 1st, 2nd, 3rd).In the pattern 1, 3, 5, 7, ..., the term '5' is at position 3 (n=3). Term ValueThe actual value or quantity of a term at a specific position in the sequence.In the pattern 10, 20, 30, ..., the term value at position 2 is '20'. Pattern RuleA description, often algebraic, that explains how to find...

Identifying the Constant Difference (Arithmetic Pattern) $d = T_n - T_{n-1}$ To find the constant difference (d) in an arithmetic growing pattern, subtract any term ($T_{n-1}$) from the term that immediately follows it ($T_n$). This 'd' represents the amount the pattern grows by each step. Finding the Nth Term of an Arithmetic Pattern $T_n = a + (n-1)d$ Use this rule to find the value of any term ($T_n$) in an arithmetic sequence. Here, 'a' is the first term, 'n' is the term number (position), and 'd' is the constant difference. This rule helps you jump to any term without listing them all. Identifying the Constant Ratio (Simple Geometric Pattern) $r = T_n / T_{n-1}$ To find the constant ratio (r) in a simple geometric growing...