4) generating sequence_from_the_nth_term

26th February 2010

Objective: to be able to generate a sequence from the nth term. (Level 6)

Skills: Making Links and Reasoning

By the end of the lesson:All: will be able to write the first 5 terms of a sequence from the nth term

Most: will be to know any term in a sequence from the nth term

Some: will be able to reason why a number can or cannot be in a sequence from the nth term

Starter

Find the nth term of the following sequences.

1. 5, 10, 15, 20, 25, ...

2. 4, 9, 14, 19, 24, ...

3. 3, 6, 9, 12, 15, ...

4. 9, 15, 21, 27, 33, ...

5. 8, 10, 12, 14, 16, ...

6. 9, 16, 23, 30, 37, ...

The Rule

• Remember what does 2n + 3 actually mean. Write the 2 steps in your books.

1. We are going up by 2’s at each step

2. At position 1 (1st term) we add 3 to 2.

Listing a sequence form the nth term

Now we understand this, see if you can list the

first 5 terms of the sequence 2n

2, 4, 6, 8, 10, ....

Listing a sequence form the nth term

Now we understand this, see if you can list the

first 5 terms of the sequence 2n + 3

5, 7, 9, 11, 13, ....

Listing a sequence form the nth term

Now we understand this, see if you can list the

first 5 terms of the sequence 5n - 3

2, 7, 12, 17, 22, ....

How can we find the nth term?

Look at the nth term:

3n

Look at the nth term:

3n – 2

Questions

• Green1. 3n-12. 4n3. 2n+74. 4n-2 5. 6n-2

• Red1. 4n-42. 5n-43. 6n-4 4. 8n+15. 6n - 10

List the first 5 terms of the following sequences from the nth term

Answers

• Green1. 2, 5, 8, 11, 142. 4, 8, 12, 16, 203. 9, 11, 13, 15, 174. 2, 6, 10, 14, 185. 4, 10, 16, 22, 28

• Red1. 0, 4, 8, 12, 162. 1, 6, 11, 16, 213. 2, 8, 14, 20, 264. 9, 17, 25, 33, 415. -4, 2, 8, 14, 20

Harder Sequences

1. -n

2. -3n

3. -4n +5

4. -5n -3

5. n²

6. n² + n

7. 3n²

Answers

1. -1, -2, -3, -4, -5, ...2. -3, -6, -9, -12, -15, ...3. 1, -3, -7, -11, -15, ...4. -8, -13, -18, -23, -285. 1, 4, 9, 16, 25, ...6. 2, 6, 12, 20, 30, ...7. 3, 12, 27, 48, 75, ...

Find nine sequences in this grid. Then match them to their nth term.

Good Luck