MYTUTOR SUBJECT ANSWERS

1654 views

How do you find the nth term formula for a sequence with non-constant difference?

Take the sequence;

9,    12,    19,    30,    ...

(1) The first step is always to look at difference between the terms;


9,    12,    19,    30,    ...
   +3,    +7,    +11,   ...                 
        +4,    +4,    ...                      

We can see the difference is not constant, (2)  so we looked at the change in the difference each term.

This gives a constant change in the difference of an extra +4 each term. The fact that we needed to take 2 turns to find the constant difference means we are dealing with a quadratic sequence.

(3) Furthermore, because the difference is +4, we are dealing with a 2n2 sequence.

If the change in the difference is (a) then the nth term follows a (1/2a)n2 pattern.

(4) Now we can rewrite the sequence as follows;

         n       n2      2n2
9       1       1         2

12     2       4         8             

19     3       9        18

30     4      16       32

 (5) We need to find the difference between the sequence and 2n2.

           2n2        d

9          2          -7                

12        8          -4                   

19       18         -1

30       32        +2

(6) The difference here will either be a constant number, in which case the nth term is (1/2a)n2 +d. Or like this case, will itself follow a linear sequence with constant difference, which we should know how to solve.

 1      2      3       4
-7,    -4,    -1,    +2
    +3     +3    +3

This gives 3n - 10. Therefore the whole formula for the nth term is;

(7) 2n2 + 3n - 10

Richard S. A Level Chemistry tutor, GCSE Chemistry tutor, GCSE Biolog...

2 years ago

Answered by Richard, a GCSE Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

330 SUBJECT SPECIALISTS

£18 /hr

Shaun F.

Degree: Mathematics with International Study (Masters) - Exeter University

Subjects offered: Maths

Maths

“Hi, I'm Shaun! I'm currently studying for a masters in Mathematics at the University of Exeter..”

MyTutor guarantee

£18 /hr

Anna G.

Degree: Dentistry (Bachelors) - Leeds University

Subjects offered: Maths, Chemistry+ 1 more

Maths
Chemistry
Biology

“Hello! I’m Anna and I’m currently studying dentistry at Leeds University. Maths was one of my favourite subjects at school and I studied it all the way up to A level. However, not everyone enjoys Maths! It’s commonly known as the trick...”

£18 /hr

Michael W.

Degree: Biomedical sciences (Bachelors) - Durham University

Subjects offered: Maths, Biology

Maths
Biology

“I am currently studying Biology at Durham University, following a passion for sciences i've had since a young age. Not everyone will instantly have the same love for these subjects as I did. But I hope through my teaching I can convey ...”

About the author

Richard S.

Currently unavailable:

Degree: MSci Natural Sciences (Masters) - Durham University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Chemistry
Biology

“Hi I'm Richard, a 2nd Year Natural Sciences student (Physics, Chemistry & Maths) reading at Durham University. Happy to help with any and all of the above as well as Biology!”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

A quarter circle represents a piece of land. The length of the straight sides is 100 ft each. If the land is enclosed by a fence, what is closest to the length, in feet, of the fence?

What's the difference between the mean, median and mode?

How do you solve the following simultaneous equation?

​What's the difference between the mean, median and mode? Why are there so many different types of average?!

View GCSE Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok