Worksheet: Nth Term of Shape Patterns

In this worksheet, we will practice recognizing a repeating pattern to say what the nth shape will be.

Q1:

What will the 16th shape in this pattern be?

  • A
  • B
  • C
  • D
  • E

Q2:

William is going to make a repeating pattern with this repeating part.

What are the first 9 shapes in this pattern?

  • A
  • B
  • C
  • D

He notices that the 3rd, 6th, and 9th shapes are all squares. He guesses that the 12th and the 15th shapes will be squares because they are multiples of 3, and there are 3 shapes in the repeated part.

Is his guess correct?

  • Ano
  • Byes

What will the 31st shape be?

  • A
  • B
  • C

Q3:

If the given pattern is extended to have 11 polygons, how many of them will be green?

Q4:

Predict how many hexagons will be present if the given pattern is extended to have a total of 38 polygons.

Q5:

Benjamin is making patterns using his baby brother’s shape tiles. He placed 1 rectangular tile followed by 2 triangular tiles and then 1 square tile in a line. He repeated this until 8 tiles were placed. How many square tiles did Benjamin use?

Q6:

How many triangles will be there when the pattern is extended to have 32 polygons?

Q7:

Olivia is making patterns of shapes using matchsticks.