Write the Terms of a Sequence From a Formula

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

Example

Find the first five 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^th term.

Answer

We get the first term, T₁, by substituting n = 1 into the T formula.

We get the second term, T₂, by substituting n = 2 into the T formula......etc.....

So...

1st term T₁ = 8 - 4 × 1 = 4
2nd term T₂ = 8 - 4 × 2 = 0
3rd term T₃ = 8 - 4 × 3 = -4
4th term T₄ = 8 - 4 × 4 = -8
5th term T₅ = 8 - 4 × 5 = -12

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

T₂₀ = 8 - 4 × 20 = 8 - 80 = -72
T₁₀₀ = 8 - 4 × 100 = 8 - 400 = -392

Are you ready to have a go at some questions?