In this worksheet, we will learn how to write the terms of a sequence from a rule known as a T formula.

__Example__

Find the first **5 terms** in the sequence given by the formula:

**T _{n} =**

**8 - 4n**

where **n** is the position of the term in the sequence.

Additionally find the** 20 ^{th}** term and the

**100**terms.

^{th}

**Answer**

We get the first term, **T**_{1}, by substituting **n = 1** in the T formula.

We get the first term, **T**_{2}, by substituting **n = 2** in the T formula......etc.....

So...

1st term T_{1} = 8 - 4 × 1 =** 4**

2nd term T_{2} = 8 - 4 × 2 = **0**

3rd term T_{3} = 8 - 4 × 3 = **-4**

4th term T_{4} = 8 - 4 × 4 =** -8**

5th term T_{5} = 8 - 4 × 5 = **-12**

Now we find the 20^{th} and 100^{th} terms.

T_{20} = 8 - 4 × 20 = 8 - 80 =** -72**

T_{100} = 8 - 4 × 100 = 8 - 400 = **-392**