Write the Terms of a Sequence From a Formula

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 - 4n²

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, 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 = 50 - 4 × 1² = 50 - 4 × 1 = 50 - 4 =  46

2nd term T₂ = 50 - 4 × 2² = 50 - 4 × 4 = 50 - 16 =  34

3rd term T₃ = 50 - 4 × 3² = 50 - 4 × 9 = 50 - 36 =  14

4th term T₄ = 50 - 4 × 4² = 50 - 4 × 16 = 50 - 64 =  -14

5th term T₅ = 50 - 4 × 5² = 50 - 4 × 25 = 50 - 100 =  -50

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

T₂₀ = 50 - 4 × 20² = 50 - 4 × 400 = 50 - 1,600 =  -1,550

T₁₀₀ = 50 - 4 × 100² = 50 - 4 × 10,000 = 50 - 40,000 =  -39,950

Let's practise this in the following questions.