#### Transcript of Nth term of linear sequences

Write an expression for the number of squares in pattern number n.

Explain how this can be found without writing down a sequence.

**Nth term of linear sequences**

Starter

Nth term of a linear pattern

How many different ways can you show this sequence has an nth term of 2n + 1?

Linear patterns

Why is this pattern linear?

**Find the nth term of linear sequences and patterns.**

Write an expression for the number of squares in pattern number n.

2n

Explain how this can be found without writing down a sequence.

The number of squares in each row is equal to the pattern number, and there are two rows.

Starter

How many squares would be in pattern number n?

How many ways can we show the expression for the nth term?

Linear patterns

Why is this pattern linear?

How many squares would be in pattern number n?

3n + 1

How many ways can we show the expression for the nth term?

n columns of 3, plus 1 square

OR

1 row of (n + 1) plus 2 rows of n

OR

1 L shape of 4 squares, plus (n - 1) columns of 3

OR the graph has gradient 3

and starts 1 square up

4 7 10 13

It goes up by 3 every time

OR

The graph is a

straight line

Nth term of a linear pattern

How many different ways can you show this sequence has an nth term of 2n + 1?

The sequence is 3, 5, 7, 9 which is 2, 4, 6, 8, (2n) add 1 (2n + 1).

Each pattern starts with 1 square and adds n lines of 2.

Each pattern starts with the original 3 squares, and add (n - 1) lines of 2.

The top row is n + 1 and the bottom row is n.

The graph goes up 2 squares, starting with 1.

Activity

Find the nth term of each of the sequences.

How many different ways can you show each one?

Activity

Find the nth term of each of the sequences.

How many different ways can you show each one?

4n + 4

4n - 3

4n + 2

Activity

5, 11, 17, 23, 29, ...

Find the nth term of this sequence

Explain how each of these calculations can arrive at the nth term

6 - 1, 12 - 1, 18 - 1, 24 - 1, 30 - 1, ...

5+ 0, 5 + 6, 5 + 12, 5 + 18, 5 + 24, ...

5+ 0, 10 + 1, 15 + 2, 20 + 3, 25 + 5, ...

Activity

5, 11, 17, 23, 29, ...

Find the nth term of this sequence

Explain how each of these calculations can arrive at the nth term

6 - 1, 12 - 1, 18 - 1, 24 - 1, 30 - 1, ... 6n - 1

5+ 0, 5 + 6, 5 + 12, 5 + 18, 5 + 24, ... 5+6(n-1)

5+ 0, 10 + 1, 15 + 2, 20 + 3, 25 + 5, ... 5n+n-1

Plenary

Draw a pattern of squares that have an nth term

of 5n + 2.

Write an explanation of how you arrived at your pattern.

**Key**

Examples

**Activities**

**Activity**

Answers

**Worked**

Example

**Worked**

Example

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