Types of sequences

The Maths Habit Handout to print

A sequence starts 2, 4, … What could the next two terms be?

6, 8: add 2 each time

8, 16: double each time

6, 10: add the two terms before

Sequence
A list of numbers that follow a rule.
Term
Each number in a sequence.
Term to term rule
How to get from one term to the next.

Linear
Add or subtract the same number each time
2, 5, 8, 11, …
Geometric
Multiply by the same number each time
3, 6, 12, 24, …
Fibonacci type
Add the two terms before
1, 1, 2, 3, 5, …
Square numbers
A number multiplied by itself
1, 4, 9, 16, …
Triangular numbers
Add one more each time
1, 3, 6, 10, …

Which type of sequence?

2, 6, 18, 54 Geometric

Linear+ or −Geometric× or ÷Fibonacci typeadd the two beforeSquare1, 4, 9, 16, …Triangular1, 3, 6, 10, …

Which type of sequence?

10, 15, 21, 28 Triangular numbers

Linear+ or −Geometric× or ÷Fibonacci typeadd the two beforeSquare1, 4, 9, 16, …Triangular1, 3, 6, 10, …

Which type of sequence?

20, 17, 14, 11, 8 Linear

Linear+ or −Geometric× or ÷Fibonacci typeadd the two beforeSquare1, 4, 9, 16, …Triangular1, 3, 6, 10, …

Which type of sequence?

25, 36, 49, 64 Square numbers

Linear+ or −Geometric× or ÷Fibonacci typeadd the two beforeSquare1, 4, 9, 16, …Triangular1, 3, 6, 10, …

Which type of sequence?

2, 5, 7, 12, 19 Fibonacci type

Linear+ or −Geometric× or ÷Fibonacci typeadd the two beforeSquare1, 4, 9, 16, …Triangular1, 3, 6, 10, …

Write what happens between each term. Tick the type. Find the next term.

1392781243× 3× 3× 3× 3
Linearadd or subtract the same number✓Geometricmultiply by the same numberFibonacci typeadd the two terms beforeSquare numbers1, 4, 9, 16, …Triangular numbers1, 3, 6, 10, …

Write what happens between each term. Tick the type. Find the next term.

512192633+ 7+ 7+ 7+ 740
✓Linearadd or subtract the same numberGeometricmultiply by the same numberFibonacci typeadd the two terms beforeSquare numbers1, 4, 9, 16, …Triangular numbers1, 3, 6, 10, …

Write what happens between each term. Tick the type. Find the next term.

145914231 + 44 + 55 + 99 + 14
Linearadd or subtract the same numberGeometricmultiply by the same number✓Fibonacci typeadd the two terms beforeSquare numbers1, 4, 9, 16, …Triangular numbers1, 3, 6, 10, …

Write what happens between each term. Tick the type. Find the next term.

1392781243× 3× 3× 3× 3
Linearadd or subtract the same number✓Geometricmultiply by the same numberFibonacci typeadd the two terms beforeSquare numbers1, 4, 9, 16, …Triangular numbers1, 3, 6, 10, …

Write what happens between each term. Tick the type. Find the next term.

474135292317− 6− 6− 6− 6
✓Linearadd or subtract the same numberGeometricmultiply by the same numberFibonacci typeadd the two terms beforeSquare numbers1, 4, 9, 16, …Triangular numbers1, 3, 6, 10, …

Write what happens between each term. Tick the type. Find the next term.

1392781243× 3× 3× 3× 3
Linearadd or subtract the same number✓Geometricmultiply by the same numberFibonacci typeadd the two terms beforeSquare numbers1, 4, 9, 16, …Triangular numbers1, 3, 6, 10, …

Write what happens between each term. Tick the type. Find the next term.

3471118293 + 44 + 77 + 1111 + 18
Linearadd or subtract the same numberGeometricmultiply by the same number✓Fibonacci typeadd the two terms beforeSquare numbers1, 4, 9, 16, …Triangular numbers1, 3, 6, 10, …

Write what happens between each term. Tick the type. Find the next term.

1392781243× 3× 3× 3× 3
Linearadd or subtract the same number✓Geometricmultiply by the same numberFibonacci typeadd the two terms beforeSquare numbers1, 4, 9, 16, …Triangular numbers1, 3, 6, 10, …

Write what happens between each term. Tick the type. Find the next term.

192964824126÷ 2÷ 2÷ 2÷ 2
Linearadd or subtract the same number✓Geometricmultiply by the same numberFibonacci typeadd the two terms beforeSquare numbers1, 4, 9, 16, …Triangular numbers1, 3, 6, 10, …

Independent task

Questions 1 to 8

Answers, questions 1 to 8

Describe the term to term rule

4, 11, 18, 25, 32 Add 7

Independent task

Questions 9 to 16

  1. Sam says 1, 2, 4, … must be a geometric sequence. Is Sam right?

    No: 1, 2, 4, 7, 11 adds 1, 2, 3, 4

  2. The 3rd term of a Fibonacci type sequence is 10. The 4th term is 16. Find the first two terms.

    4, 6

  3. A geometric sequence starts 3, 6, 12, … What is the first term that is bigger than 1000?

    1,536

Answers, questions 9 to 16

Four Fours puzzle

Sort the cards into four groups of four.

Puzzle to print

1=
2=
3=
4=

Types of sequences worksheet, page 1

Types of sequences worksheet, page 2

Answer sheet

  1. Name the type of sequence and find the next term: 2, 7, 9, 16, 25

    Fibonacci type, 41

  2. Name the type of sequence and find the next term: 2, 6, 18, 54

    Geometric, 162

  3. Describe the term to term rule: 81, 27, 9, 3

    Divide by 3

  4. Is 1, 4, 16, 64 square numbers or geometric? Give a reason.

    Geometric: multiply by 4 each time
Exit tickets to print