Write variable expressions for arithmetic sequences

Learning Objectives Identify a pattern in a list of numbers as an arithmetic sequence. Determine the 'rule' (common difference) of an arithmetic sequence. Use a variable, like 'n', to represent the position of a number in a sequence. Write a variable expression that connects the position number (n) to the term value for simple sequences (e.g., n * 5). Write a two-step variable expression for more complex arithmetic sequences (e.g., (n * 2) + 1). Use a written variable expression to find the value of a specific term in a sequence. Imagine you're building a tower with blocks, adding 3 blocks to each new level. How could you figure out how many blocks the 100th level has without building it? 🧱 In this lesson, we will explore number patterns called ari...

TermDefinitionExample SequenceA list of numbers that follow a specific order or pattern.2, 4, 6, 8, 10, ... TermEach individual number in a sequence.In the sequence 2, 4, 6, 8, the number 6 is the 3rd term. Arithmetic SequenceA sequence where you add or subtract the same number every time to get to the next term.5, 10, 15, 20, ... (The pattern is to add 5 each time). Rule (Common Difference)The number that is repeatedly added in an arithmetic sequence.In the sequence 3, 6, 9, 12, the rule is 'add 3'. VariableA letter or symbol that represents a number that can change. We often use 'n' to stand for the term's position number.In our sequence, 'n' could be 1 for the 1st term, 2 for the 2nd term, and so on. Variable ExpressionA math phrase with variables, nu...

Position-to-Term Rule (Simple Multiplication) \text{Term Value} = n \times d Use this for simple sequences that start at the common difference (d) and go up by that amount. Here, 'n' is the term's position (1, 2, 3...) and 'd' is the rule. For the sequence 7, 14, 21..., the rule is 'add 7', so the expression is n * 7. Position-to-Term Rule (Two-Step) \text{Term Value} = (n \times d) + \text{adjustment} Use this when the simple multiplication rule doesn't work. First, multiply the position 'n' by the rule 'd'. Then, see what number you need to add or subtract to get the correct term value. That is your 'adjustment'.