Find the Terms of a Sequence from a Formula with a Quadratic Term

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 = 2n² − 3n + 5

we simply substitute different values for n.

The first term is called T₁ , where n = 1.

The second term is called T₂ , where n = 2 etc.

The twentieth term is called T₂₀ , where n = 20.

Examples

T₁ = (2 × 1²) − (3 × 1) + 5 = 4

T₂ = (2 × 2²) − (3 × 2) + 5 = 7

T₃ = (2 × 3²) − (3 × 3) + 5 = 14

T₄ = (2 × 4²) − (3 × 4) + 5 = 25

T₅ = (2 × 5²) − (3 × 5) + 5 = 40

T₂₀ = (2 × 20²) − (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.