Hi Grant,

Rather than doing one of your homework question I am going to do a similar problem. I am going to look at

3n - 2

The letter n stands for the number of the term in the sequence. For example

For the first term, n = 1; so 3n - 2 = 3 1 - 2 = 3 - 2 = 1
For the second term, n = 2; so 3n - 2 = 3 2 - 2 = 6 - 2 = 4
For the third term, n = 3; so 3n - 2 = 3 3 - 2 = 9 - 2 =7
For the fourth term, n = 4; so 3n - 2 = 3 4 - 2 = 12 - 2 = 10
etc.

So the value of the firsat four terms arre

1, 4, 7, 10

If you are given the term 3n - 2 and you want the next five terms then these are the terms numbered

n + 1; n + 2; n + 3; n + 4 and n + 5

Thus the values are

3(n + 1) - 2 = 3n + 3 - 2 = 3n + 1
3(n + 2) - 2 = 3n + 6 - 2 = 3n + 4
3(n + 3) - 2 = 3n + 9 - 2 = 3n + 7
etc

To explain the sequence in words I would say that the value of a term is 3 time the term number minus 2. Thus, for example, the value of the ninth term is

3 9 - 2 = 27 - 2 = 25

Penny