Arithmetic and geometric sequences – Grade 11 math lesson

Lesson 8 of 23 in the Grade 11 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 11 (ages 16–17) 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 11 (ages 16–17)
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

45 minutes in 5 parts
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

All Grade 11 math lessons and tests · Math Department

Curriculum

Common Core State Standards HSA.SSE.B.4: “Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*”

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.*”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.