Arithmetic sequences

Learning Objectives Define an arithmetic sequence and identify its key components. Determine the common difference of an arithmetic sequence. Write the explicit formula for the nth term of an arithmetic sequence. Use the explicit formula to find the value of any term in a sequence. Find the number of terms in a finite arithmetic sequence. Model and solve real-world problems using arithmetic sequences. If you save $5 in week one, $8 in week two, and $11 in week three, how much will you save in week 20? 💰 Let's find out! This tutorial introduces arithmetic sequences, which are ordered lists of numbers with a constant difference. You will learn how to identify these patterns, write a formula to describe them, and use that formula to make predictions. This is a key buildi...

TermDefinitionExample SequenceAn ordered list of numbers, often following a specific pattern or rule.2, 4, 6, 8, 10, ... TermEach individual number in a sequence. We use subscript notation like a₁, a₂, a₃ to denote the first, second, and third terms.In the sequence 5, 10, 15, 20, the third term (a₃) is 15. Arithmetic SequenceA sequence in which the difference between any two consecutive terms is constant.3, 7, 11, 15, 19, ... (The difference is always 4). First Term (a₁)The very first number in a sequence.In the sequence 10, 8, 6, 4, ..., the first term (a₁) is 10. Common Difference (d)The constant value that is added to each term to get the next term in an arithmetic sequence. It can be positive or negative.In the sequence 50, 45, 40, 35, ..., the common difference (d) is -5. nth Term (a...

Finding the Common Difference d = a_n - a_{n-1} To find the common difference (d), subtract any term from the term that immediately follows it. For example, d = a₂ - a₁ or d = a₅ - a₄. The Explicit Formula for an Arithmetic Sequence a_n = a_1 + (n - 1)d This is the most important formula for arithmetic sequences. It allows you to find the value of any term (aₙ) if you know the first term (a₁), the position of the term you want (n), and the common difference (d).