3.10 Arithmetic Sequences — Predict the Future with a Simple Formula | Contemporary Mathematics

• Learn the definition of an arithmetic sequence, its terms, and the constant difference.
• Learn to use the nth term formula to find any term in an arithmetic sequence.
• Discover how to find the constant difference and first term from any two terms.
• Learn Gauss's method to quickly calculate the sum of a finite arithmetic sequence.
• Explore how arithmetic sequences apply to habit building, savings, and training goals.
• Contrast arithmetic sequences with the recursive Fibonacci sequence and its presence in nature.
• Up next in “Contemporary Math — Full Course (OpenStax)”3.11 Geometric Sequences — The Math That Makes Wealth Explode | Contemporary Mathematics

Arithmetic sequences show up everywhere — from the 2.5 quintillion bytes of data added to the internet every single day, to savings plans, marathon training, and data center projections. This lesson from Section 3.10 of OpenStax Contemporary Mathematics breaks down the core mechanics of arithmetic sequences: what they are, how to use them, and why they matter in the real world. Whether you're predicting a future term, reverse-engineering a missing starting point, or calculating a year's worth of accumulated savings, this video gives you the tools to do it all. In this video: • What makes a sequence "arithmetic" — the constant difference (d) and why it creates total predictability • The ith term formula explained: why the exponent uses (i − 1) and not i, using a sequence starting at 4 with d = 3 • How to reverse-engineer an arithmetic sequence from just two data points — demonstrated with a server usage scenario (month 7: 56 TB, month 19: 104 TB) • The summation formula and its origin in Carl Friedrich Gauss's childhood trick of pairing terms to find the sum from 1 to 100 • Applying all three tools to Christina's savings plan: starting at $10/week with a $5 weekly increase leads to $7,150 accumulated in one year • Real-world applications including Jordan's chess practice schedule, Jasmyn's running mileage, and internet data growth • The Fibonacci sequence as a contrast to arithmetic growth — recursive, compounding, and found in sunflowers, nautilus shells, and even music #OpenStax #ArithmeticSequences #ContemporaryMathematics #Math #LinearGrowth OpenStax Content adapted from "Contemporary Math", by OpenStax Licensed under CC BY 4.0. Content based on Web Version: Apr 23, 2026. Read the textbook online https://openstax.org/details/books/contemporary-mathematics Music first girl talking to me. by ikkun (ex. Barradeen) | https://soundcloud.com/ikkunwastaken Royalty Free Music by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US