Find terms of an arithmetic sequence

Learning Objectives Define an arithmetic sequence and identify its first term (a₁) and common difference (d). Apply the explicit formula for the nth term of an arithmetic sequence. Calculate any specified term (the nth term) of a given arithmetic sequence. Determine the first term or common difference when given two non-consecutive terms. Find the number of terms in a finite arithmetic sequence. Solve word problems by modeling them with arithmetic sequences. Imagine you start a savings plan by putting $10 in a jar, and you add $5 more each week. How much money will you add on the 52nd week? 💰 This tutorial explores arithmetic sequences, which are ordered lists of numbers where the difference between consecutive terms is constant. You will master the formula to find any ter...

TermDefinitionExample SequenceAn ordered list of numbers, often following a specific pattern or rule.2, 4, 8, 16, 32, ... TermAn individual number or element in a sequence. The notation aₙ refers to the term in the nth position.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 100, 90, 80, ..., the first term (a₁) is 100. 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, negative, or zero.In the sequence 50, 47, 44, 41, ..., the common difference (d) is -3. nth Term (aₙ)The general t...

The nth Term Formula (Explicit Formula) aₙ = a₁ + (n - 1)d This is the fundamental formula used to find the value of any term (aₙ) in an arithmetic sequence if you know the first term (a₁), the term's position (n), and the common difference (d). Common Difference Formula d = aₙ - aₙ₋₁ To find the common difference, subtract any term from the term that immediately follows it. This is useful for identifying 'd' from a given list of terms. Finding 'd' from Non-Consecutive Terms d = (aₘ - aₙ) / (m - n) A powerful shortcut to find the common difference when you are given two terms (aₘ and aₙ) and their positions (m and n) but not the first term.