Arithmetic Sequences | Integrated Math 1 (2026 Update) скачать в хорошем качестве

Arithmetic Sequences | Integrated Math 1 (2026 Update)

In this lesson (3.4 Arithmetic Sequences) we introduce arithmetic sequences—sequences where each term changes by the same constant amount called the common difference (d). We go over how to identify an arithmetic sequence by checking differences, then learn the two main ways to write them: Recursive form (uses the previous term): ​ with a starting value Explicit form (jump straight to any term): We practice writing recursive formulas from patterns, writing explicit formulas from tables, and using explicit formulas to find specific terms (like the 10th or 17th term). We also connect arithmetic sequences to linear functions by building a table, graphing the points, writing the line equation, and showing how the explicit formula matches the linear equation. Finally, we convert recursive → explicit and explicit → recursive. 🔗 Visit www.clopensets.com for full class videos, guided notes, and printable worksheets that go along with this lesson. 🔗 ClopenSets shop: https://www.etsy.com/shop/Clopensets #education #maths #math #highschoolmath #highschool Chapters: 00:00 What is an arithmetic sequence? (common difference) 00:28 Recursive vs. explicit formulas (why we use each) 00:59 Notation 01:44 Determine if a list is arithmetic (check differences) 02:09 Sequences as functions (domain = natural numbers) 02:46 What “recursive” means + recursive formula structure 03:20 Example: write a recursive formula (pyramid steps, +26) 04:43 Write a recursive formula with negative difference (−3) 05:24 Explicit formula and what each part means 05:57 Example: write explicit formula from a table (bike rental) 07:17 Use explicit formula to find a specific term (10th term) 07:45 Practice: explicit formula + simplify + find 17th term 08:55 Sequences ↔ linear functions (table, graph, line equation) 10:39 Match explicit formula to the line equation (same rule) 11:21 Convert recursive → explicit 12:07 Convert explicit → recursive