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Write the Terms of a Sequence From a Formula

In this worksheet, students find the required terms of a sequence from the given T formulae.

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

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Generate Terms of a Sequence

Difficulty level:  

Worksheet Overview

In this worksheet, 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 in the T formula.

We get the second term, T2, by substituting n = 2 in 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 - 1600 =  -1550

T100 = 50 - 4 × 1002 = 50 - 4 × 10000 = 50 - 40000 =  -39950

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