Arithmetic and geometric sequences – Grade 9 math lesson
Lesson 13 of 17 in the Grade 9 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 9 (ages 14–15) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 9 (ages 14–15)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Is 100 a term in the sequence 3n + 2? How can you tell?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using the difference as the whole nth term (5, 8, 11… is 3n). Check n = 1: 3 × 1 = 3, so add 2.
- Treating a geometric sequence as linear. Check differences and ratios.
Tip for home: Look for sequences in nature, such as petals and spirals.
What your child will learn
Learning goal: find and use the nth term of sequences and recognize special sequences.
Success looks like
- I can find the nth term of a linear sequence.
- I can use the nth term to find any term.
- I can recognize geometric and special sequences.
Key words
- term
- one number in a sequence
- nth term
- a rule for any term from its position
- common difference
- the amount added each time
- common ratio
- the amount multiplied each time
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Build a pattern of growing shapes with matchsticks and find the rule for the nth pattern.
The big ideas (for the adult)
A linear sequence goes up by the same amount each time. Its nth term is dn + c, where d is the common difference: 5, 8, 11… has nth term 3n + 2.
A geometric sequence multiplies by the same number each time: 3, 6, 12, 24…
Other sequences include square numbers, triangular numbers and Fibonacci-type sequences, where each term is the sum of the two before.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 9 math lessons
Curriculum
Common Core State Standards HSF.BF.A.2: “Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*”
Common Core State Standards HSF.IF.A.3: “Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.