Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Write the Terms of a Sequence From a Formula

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

'Write the Terms of a Sequence From a Formula' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Algebra

Curriculum subtopic:   Generate Terms of a Sequence

Difficulty level:  

Worksheet Overview

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:

 

Tn = 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 20th and 100th 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.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Try an activity or get started for free

  • National Tutoring Awards 2023 Shortlisted / Parents
    National Tutoring Awards 2023 Shortlisted
  • Private-Tutoring-WINNER-EducationInvestor-Awards / Parents
    Winner - Private Tutoring
  • Bett Awards Finalist / Parents
    Finalist
  • Winner - Best for Home Learning / Parents
    Winner - Best for Home Learning / Parents