This activity is about finding terms of a sequence from a formula with a quadratic term.

To find the first 5 terms and the 20th term of the sequence given by the formula

**T _{n }= 2n^{2} − 3n + 5**

we simply substitute different values for n.

The first term is called **T _{1 }**, where

**n = 1**.

The second term is called **T _{2 }**, where

**n = 2**etc.

The twentieth term is called **T _{20}** , where

**n = 20**.

**Examples**

**T _{1}** = (2 × 1

^{2}) − (3 × 1) + 5 =

**4**

**T _{2}** = (2 × 2

^{2}) − (3 × 2) + 5 =

**7**

**T _{3}** = (2 × 3

^{2}) − (3 × 3) + 5 =

**14**

**T _{4}** = (2 × 4

^{2}) − (3 × 4) + 5 =

**25**

**T _{5} **= (2 × 5

^{2}) − (3 × 5) + 5 =

**40**

**T _{20}** = (2 × 20

^{2}) − (3 × 20) + 5 =

**745**

It might look a bit daunting, but just take it slowly, one step at a time and you'll soon be flying through them!

Let's get started.