Write variable expressions for arithmetic sequences

Learning Objectives Identify an arithmetic sequence. Determine the common difference of an arithmetic sequence. Recall and apply the formula for the nth term of an arithmetic sequence. Substitute known values into the nth term formula. Simplify algebraic expressions to write a variable expression for an arithmetic sequence. Use a variable expression to find any term in an arithmetic sequence. Ever noticed patterns in numbers, like the number of seats in rows at a concert or the amount of money saved each week? 💰 What if we could write a rule to predict any number in that pattern? In this lesson, you'll learn how to identify special number patterns called arithmetic sequences and, more importantly, how to write a powerful variable expression that describes them. This e...

TermDefinitionExample SequenceAn ordered list of numbers.2, 4, 6, 8, 10, ... TermEach individual number in a sequence.In the sequence 2, 4, 6, 8, ..., 2 is the 1st term, 4 is the 2nd term, and so on. Arithmetic SequenceA sequence where the difference between consecutive terms is constant.3, 7, 11, 15, ... (The difference between each term is 4). Common Difference (d)The constant difference between consecutive terms in an arithmetic sequence. It can be positive, negative, or zero.In the sequence 10, 8, 6, 4, ..., the common difference (d) is -2. Variable ExpressionA mathematical phrase that contains numbers, variables (like 'n'), and operation symbols, but no equality sign.For an arithmetic sequence, a variable expression might look like `3n + 2`. Position (n)A variable, usually...

Formula for the nth Term of an Arithmetic Sequence $$a_n = a_1 + (n-1)d$$ This formula allows you to find the value of any term ($a_n$) in an arithmetic sequence. $a_1$ is the first term, $n$ is the position of the term you want to find, and $d$ is the common difference. Finding the Common Difference $$d = a_k - a_{k-1}$$ To find the common difference ($d$), subtract any term ($a_{k-1}$) from the term that directly follows it ($a_k$). This difference should be constant throughout the sequence.