The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Find the Formula for the General Term, Tn, of a Sequence

In this worksheet, studends find the formula for the general term, Tn, of a sequence.

'Find the Formula for the General Term, Tn, of a Sequence' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In this worksheet, we will learn how to find the formula for the general term, Tn, of a sequence.

 

Example

Term no., n =                   1           2            3            4            5
Term, Tn=                        4           8           12          16          20
Common difference =           +4          +4          +4         +4

 

It is clear, that Tn = 4n.

Also note that the difference between each term is 4.

 

Compare this sequence with the one below:

Term no., n =                   1            2            3            4            5
Term, Tn=                        7           11          15          19          23
Common difference =           +4          +4           +4          +4

 

The common difference of +4 tells us that this sequence is "related" to the first one .

It begins Tn = 4n... and so is in the 4n "family".


Compare the two and you will see that each term is 3 more than that in the first sequence. 

7 = 4 + 3
11 = 8 + 3
15 = 12 + 3


So Tn = 4n + 3

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

9 14 19 24 29  

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

   9  17 25 33 41  

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

  3 11 19 27 35  

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

 6 8 10 12 14  

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

5 12 19 26 33  

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

-2 1 4 7 10  

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

6 11 16 21 26  

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

-1 2 5 8 11  

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

12 20 28 36 44  

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

1 5 9 13 17  
  • Question 1

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

9 14 19 24 29  
CORRECT ANSWER
5n+4
5n + 4
  • Question 2

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

   9  17 25 33 41  
CORRECT ANSWER
8n+1
8n + 1
  • Question 3

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

  3 11 19 27 35  
CORRECT ANSWER
8n-5
8n - 5
  • Question 4

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

 6 8 10 12 14  
CORRECT ANSWER
2n+4
2n + 4
  • Question 5

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

5 12 19 26 33  
CORRECT ANSWER
7n-2
7n - 2
  • Question 6

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

-2 1 4 7 10  
CORRECT ANSWER
3n-5
3n - 5
  • Question 7

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

6 11 16 21 26  
CORRECT ANSWER
5n+1
5n + 1
  • Question 8

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

-1 2 5 8 11  
CORRECT ANSWER
3n-4
3n - 4
  • Question 9

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

12 20 28 36 44  
CORRECT ANSWER
8n+4
8n + 4
  • Question 10

Find the Tn formula for the following sequence, in which the first five terms are shown.  

 

Tn = _________

 

1 5 9 13 17  
CORRECT ANSWER
4n-3
4n - 3
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

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

Start your £1 trial today.
Subscribe from £10/month.