Sequences and the Nth term

Copy each of these sequences into your books.

a) Write the next two terms of each sequence                                                                             

b) Write the term to term rule (how do you get from one term to the next)

(watch the video below if you need help)

  1. 3, 7, 11, 15...
  2. -3, 2, 7, 12...
  3. 3, 6, 12, 24...
  4. 10, 7, 4, 1...
  5. 1, 1, 2, 3, 5 ...

Any sequence which goes up or down in equal steps is called an arithmetic or linear sequence.

Sequences 1, 2, 4, 6  and 8 from above are examples of these.

Sometimes you will be asked to find missing terms in a sequence:

Find the missing terms in these sequences

  1. 3, __, 7, 9, ...
  2. 4, 7, 13, __, 49, __ ...
  3. 4, __, __, 19 ... (if the sequence increases by the same amount each time)
  4. 3, __,  __, __, 11 ... (if the sequence increases by the same amount each time)
  5. 12, __, __, -6 ... (if the sequence decreases by the same amount each time)

The Nth Term

Here is another arithmetic sequence 5, 7, 9, 11, 13... how would I find the 40th term in this sequence? Write it down and the method you used.

The best way to do this is to link a terms position to its value.  To do this we find a

Watch the video below (until 12.26) and attempt the questions set in your books (pause before the answers are given)

Now go to diagnostic questions (link below) login and complete the assignment Sequences - Nth Term

Quadratic Sequences

Take a look at these sequences? What do you notice about them? Can you find the next 3 terms?

1) 1, 4, 9, 16, 26...

2) 5, 12, 21, 32...

3) 0, 9, 22, 39....

Quadratic Discovery

If you are stuck have a look at this video to get you started.

Extension

Plenary