In this activity, we will work out some of 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} =**

**50 - 4n**

^{2}

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

Additionally find the** 20th** term and the **100th** term.

**Answer**

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

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

So...

1st term **T _{1}** = 50 - 4 × 1

^{2}= 50 - 4 × 1 = 50 - 4 =

**46**

2nd term **T _{2}** = 50 - 4 × 2

^{2}= 50 - 4 × 4 = 50 - 16 =

**34**

3rd term **T _{3}** = 50 - 4 × 3

^{2}= 50 - 4 × 9 = 50 - 36 =

**14**

4th term **T _{4}** = 50 - 4 × 4

^{2}=

**50 - 4 × 16 = 50 - 64 =**

**-14**

5th term **T _{5}** = 50 - 4 × 5

^{2}= 50 - 4 × 25 = 50 - 100 =

**-50**

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

**T _{20}** = 50 - 4 × 20

^{2}= 50 - 4 × 400 = 50 - 1,600 =

**-1,550**

**T _{100}** = 50 - 4 × 100

^{2}= 50 - 4 × 10,000 = 50 - 40,000 =

**-39,950**

Let's practise this in the following questions.