Richard S.

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Degree: MSci Natural Sciences (Masters) - Durham University

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Hi my name is Richard and I'm a science student currently at Durham. People say the best way to prove that you understand something well is to be able to teach it to someone else. With my background and future ambitions in science I aim to do just that :) ​

I have been tutoring for many years, whether officially through organisations such as MyTutorWeb or unofficially helping friends and family with their work; my teachers would often remark that I was destined to become a teacher at some stage in my life!

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Fluid one to one sessions whereby we follow the curricula through, with frequent exam practice to hone technique, recognise patterns and really lock the knowledge in the brain. Equally, should there be any specific topics or questions that you wish to look at then the time is completely yours to direct us where you need the guidance most.

Thank you for taking the time to check me out!

Subjects offered

SubjectLevelMy prices
Chemistry A Level £20 /hr
Maths A Level £20 /hr
Physics A Level £20 /hr
Biology GCSE £18 /hr
Chemistry GCSE £18 /hr
Maths GCSE £18 /hr
Physics GCSE £18 /hr

Qualifications

ChemistryA-LevelA*
BiologyA-LevelA*
MathsA-LevelA*
Further MathsA-LevelA
PhysicsA-LevelA
 CRB/DBS Standard No CRB/DBS Enhanced ✓ 25/11/2013

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)  ...

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

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2 years ago

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