An arithmetic sequence is a list of numbers (terms) with a constant difference (d) between each term. You add the same number to get from one term to the next.
Notes
Practice Problems
\(\textbf{1)}\) Find the next three terms of the sequence \(3, 7, 11,\ldots\) 
\(\textbf{2)}\) Find the next four terms of the sequence \(45, 38, 31,\ldots\)
\(\textbf{3)}\) Find the rule of the sequence \(3, 7, 11,\ldots\)
\(\textbf{4)}\) Find the rule of the sequence \(45, 38, 31,\ldots\)
Find the missing value
\(\textbf{5)}\) \(a_1=3,\,d=5,\,\) what is \(a_8\)?
\(\textbf{6)}\) \(d=-2,\, a_5=10,\,\) what is \(a_1\)?
\(\textbf{7)}\) \(a_1=7,\, a_6=22,\,\) what is \(d\)?
Challenge Problem
\(\textbf{8)}\) Find the three arithmetic means of \(3\) and \(48\)
See Related Pages
\(\bullet\text{ Geometric Sequences}\)
\(\,\,\,\,\,\,\,a_n=a_1 \cdot r^{(n-1)}…\)
\(\bullet\text{ Arithmetic Series}\)
\(\,\,\,\,\,\,\,s_n=\frac{n}{2}(a_1+a_n)…\)
\(\bullet\text{ Geometric Series}\)
\(\,\,\,\,\,\,\,s_n=a_1 \frac{1-r^n}{1-r}…\)
\(\bullet\text{ Infinite Geometric Series}\)
\(\,\,\,\,\,\,\,s_\infty = \frac{a_1}{1-r}\,\,\, |r| \lt 1…\)
\(\bullet\text{ Summation Notation}\)
\(\,\,\,\,\,\,\, \displaystyle \sum_{i=4}^{9} 3i-5 …\)
\(\bullet\text{ Recursive Sequences}\)
\(\,\,\,\,\,\,\, a_{1}=2, \, a_{n+1}=a_{n}+3…\)
\(\bullet\text{ Andymath Homepage}\)
About Andymath.com
Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.
Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.
Visit me on Youtube, Tiktok, Instagram and Facebook. Andymath content has a unique approach to presenting mathematics. The clear explanations, strong visuals mixed with dry humor regularly get millions of views. We are open to collaborations of all types, please contact Andy at tutoring@andymath.com for all enquiries. To offer financial support, visit my Patreon page. Let’s help students understand the math way of thinking!
Thank you for visiting. How exciting!