**Defining Sequences**

Starter

Two sequences are defined as

3n + 8

5n - 2

After which term does the second sequence become bigger than the first?

Linear Sequences

Find the nth term of this sequence:

3, 10, 17, 24, 31, ...

Linear Sequences (continued)

Find the nth term of this sequence:

26, 22, 18, 14, 10, ...

**L.O. - To find the position-to-term rule for a sequence, and use this ability to find formulae.**

5, 9, 13, 17, 21, ....

2, 8, 14, 20, 26, ....

18, 11, 4, -3, -10, ...

-3, 4, 11, 18, 25, ...

Main Activity 1

Red

Amber

Green

Find a formula linking

the width of the pattern and the number of squares

the width of the pattern and the perimeter of the pattern.

Find the nth term of:

3, 7, 11, 15, ....

8, 11, 14, 17, ...

Find the nth term of:

2, 9, 16, 23, ...

23, 16, 9, 2, ...

8, -1, -10, -19, ...

100, 97, 94, 91, ....

Find a formula connecting the number of

rectangles with the number of matchsticks.

Find the nth term of

this sequence:

3, ...., ....., ....., ....., 48

Find the nth term of:

6, 13, 20, 27, 34, ...

9, 15, 21, 27, 33, ...

Find the nth term of:

1, 8, 15, 22, 29, ...

5, 16, 27, 38, 49, ...

Find a formula connecting the number of squares with the perimeter.

2, 11, 20, 29, .....

Find the nth term of the sequence.

Find the first term greater than 100.

111, 102, 93, 84, ....

Find the nth term of the sequence

Find the first negative term of the sequence.

Main Activity 1

Red

Amber

Green

4n -1

3n + 5

7n -1

6n + 3

7n -6

11n -6

P = 3s + 1

7n - 5

-7n + 30 (30 - 7n)

-9n + 17 (17 - 9n)

-3n + 103 (103 - 3n)

9n - 7

101 (12th term)

9n - 6

-9n + 130 (130 - 9n)

-5 (15th term)

M = 11r

Linear Sequences

Find the nth term of these linear sequences

Linear Sequences (continued)

Starter

Two sequences are defined as

3n + 8 = 11, 14, 17, 20, 23,

26

, 29, 32, ...

5n - 2 = 3, 8, 13, 18, 23,

28

, 33

After which term does the second sequence become bigger than the first?

After the 6th term

Find a formula linking

the width of the pattern and the number of squares. -

S = 2w - 1

the width of the pattern and the perimeter of the pattern. -

P = 4w

Linear Sequences

Find the nth term of this sequence:

3, 10, 17, 24, 31, ...

= 7n - 4

7, 14, 21, 28, 35, ... = 7n

5, 9, 13, 17, 21, ....

= 4n + 1

2, 8, 14, 20, 26, ....

= 6n - 4

Linear Sequences

Find the nth term of these linear sequences

4 8 12 16 20 .... = 4n

6 12 18 24 28 .... = 6n

Linear Sequences (continued)

Find the nth term of this sequence:

26, 22, 18, 14, 10, ...

= -4n + 30 = 30 - 4n

-4, -8, -12, -16, -20, ... = -4n

18, 11, 4, -3, -10, ...

= -7n + 25

-3, 4, 11, 18, 25, ...

= 7n - 10

Linear Sequences (continued)

-7,-14, -21, -28, -35, ... = -7n

7, 14, 21, 28, 35, ... = 7n

**Activities**

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