## MYTUTOR SUBJECT ANSWERS

14383 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

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

#### 780 SUBJECT SPECIALISTS

£18 /hr

Degree: MSc Financial Analysis and Fund Management (Masters) - Exeter University

Subjects offered:Maths, Economics

Maths
Economics

“1st Class Economics Graduate and Postgraduate student with broad tutoring experience - let me help you achieve!”

£18 /hr

Degree: Economics and Accounting (Bachelors) - Bristol University

Subjects offered:Maths, Economics

Maths
Economics

“I achieved top grades whilst juggling cricket at a high level. I’ve tutored for Young Einstein Tuition & been a Peer Mentor to those facing personal issues”

£36 /hr

Degree: Computer Science (Doctorate) - Manchester University

Subjects offered:Maths, Italian+ 3 more

Maths
Italian
ICT
Computing
-Personal Statements-

“PhD Student in Computer Science with a passion for interdisciplinary research and teaching”

#### About the author

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

Solve the simultaneous equations: 4x+5y = 38 , x-y = 5

When I multiple two negative numbers together is my answer positive or negative?

Expand and simplify (x+6)(x-6)

Factorise and solve x^2 - 8x + 15 = 0

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.