Write variable expressions for arithmetic sequences

Learning Objectives Identify an arithmetic sequence. Determine the common difference of an arithmetic sequence. Identify the first term of an arithmetic sequence. Write a variable expression for the nth term of a given arithmetic sequence. Use a variable expression to find any term in an arithmetic sequence. Simplify variable expressions for arithmetic sequences. Have you 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 find any number in that pattern? In this lesson, you'll learn how to describe special number patterns called arithmetic sequences using variable expressions. This skill will help you predict future numbers in a pattern without listing them all out,...

TermDefinitionExample SequenceAn ordered list of numbers.2, 4, 6, 8, ... TermEach individual number in a sequence.In the sequence 2, 4, 6, 8, ..., the number 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, 6, 9, 12, ... (The difference between terms is always 3) Common Difference (d)The constant difference between consecutive terms in an arithmetic sequence. It's found by subtracting any term from the term that follows it.In 3, 6, 9, 12, ..., the common difference (d) is 6 - 3 = 3 (or 9 - 6 = 3). First Term (a_1)The very first number in an arithmetic sequence.In 3, 6, 9, 12, ..., the first term (a_1) is 3. Variable ExpressionA mathematical phrase that contains numbers, variables (like 'n...

Formula for the Common Difference $$d = a_2 - a_1$$ To find the common difference (d) of an arithmetic sequence, subtract the first term ($a_1$) from the second term ($a_2$). You can also subtract any term from the term immediately following it. Formula for the nth Term of an Arithmetic Sequence $$a_n = a_1 + (n-1)d$$ This is the main formula to write a variable expression for any term ($a_n$) in an arithmetic sequence. Here, $a_1$ is the first term, $n$ is the term number you want to find, and $d$ is the common difference. You will substitute $a_1$ and $d$ into this formula and simplify to get your expression.