 # 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. Key stage:  KS 3

Curriculum topic:   Algebra

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

Difficulty level:   ### 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
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
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
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
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
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
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
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
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
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
4n-3
4n - 3
---- OR ----

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