# Write the Terms of a Sequence From a Formula

In this worksheet, students will find the first few terms of a sequence from the given T formula.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Generate Terms of a Sequence

Popular topics:   Algebra worksheets, Year 7 Algebra worksheets

Difficulty level:

#### Worksheet Overview

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:

Tn = 8 - 4n

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

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

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 20th and 100th 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?

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