I feel so unconfident with sequences;/ like I know how to work out the normal kinds of nth terms but there are really hard ones and i also don't understand some of the questions.. is there a method to work out the sequences or formulas i can learn?? Im having trouble with summer 07 p4 Q9, part b) ii) and all of part c) ;/?? HELP!! would be much appreciated!!
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MATHS SEQUENCES !!!!
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the formula for the nth term is, a+(n-1)d
'a' stands for the first number of the sequence
'd' stands for difference between the sequence
i gave u a solved one
hope this helps
'a' stands for the first number of the sequence
'd' stands for difference between the sequence
i gave u a solved one
hope this helps
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Good work Adeel! It makes your first post very helpful 
...
The formula for quadratic equation is a+(n-1)d1+1/2(n-1)(n-2)d2
a is the first term of sequence
d1 1st difference
d2 2nd difference...
Put and solve...
...The formula for quadratic equation is a+(n-1)d1+1/2(n-1)(n-2)d2
a is the first term of sequence
d1 1st difference
d2 2nd difference...
Put and solve...
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The second difference here mean take the difference again... In your case it's 2,2,2....
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CaprainDanger ur quadratic quation is differnt from mine
or u simplify it ??
or u simplify it ??
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ohh i never knew this thread
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what math is this ???
hw come i never saw it ??
hw come i never saw it ??
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Neither Did I... Came here... Learnt it...
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There is an easy way to find the formula for the second difference. Perhaps what I am going to tell you isn't mention anywhere in the textbooks so note it down and keep it safe for future generations!
As for finding the formula for the sequence like this :- 2,4,7,11 etc....
It is this :- 0.5(n^2)-0.5n+1
(2nd difference of the sequence/2)x(n^2)-nth formula
First you will take (1/2)x(n^2) and then find the nth formula . For finding the nth formula first do this rough working.
The first term of this sequence is 1 and how is that? Since 2,4 has a first difference of 2 and 4,7 has a difference of 3 . The second difference of 2 and 3 is 1. That is why I took (1/2) in the formula for the second difference. If you subtract 1 from 2 , you will get the difference of 1st term and 2nd term which will give you the first term of this sequence which is 1. It is important that the first difference should be one before you start the working because these are second difference sequences. In the first difference type of sequences, they can start with any number. But in these you have to be careful! So whenever you are doing any questions of second difference , always see that any term you have has a first difference of 1!
Having explained that, I will now tell you how to find the nth formula. We know that Nth formula is An= a+(n-1)d
'a' is the first difference of the term. 'd' is the difference of the 2nd and the 1st term.
The working for this is nth term number - (2nd a/2)(nth term)^2 = whatever the answer is.
e.g 1) 1-(0.5)(1)^2 = 0.5
2) 2-(0.5)(2)^2= 0
3) 4-(0.5)(3)^2 = -1/2
d= 2nd term - 1st term or 3rd term - 2nd term
d= -0.5 , a= 1/2
An = a+(n-1)(d)
An= 0.5+(n-1)(-0.5)
An= 1/2+1/2 - 0.5n
An= -1/2+1
Now you have found the nth formula. Add this into the one that I found earlier.
It will be 0.5(n^2)-0.5n+1
The sequence is 1,2,4,7,11,16
Happy day everyone!
As for finding the formula for the sequence like this :- 2,4,7,11 etc....
It is this :- 0.5(n^2)-0.5n+1
(2nd difference of the sequence/2)x(n^2)-nth formula
First you will take (1/2)x(n^2) and then find the nth formula . For finding the nth formula first do this rough working.
The first term of this sequence is 1 and how is that? Since 2,4 has a first difference of 2 and 4,7 has a difference of 3 . The second difference of 2 and 3 is 1. That is why I took (1/2) in the formula for the second difference. If you subtract 1 from 2 , you will get the difference of 1st term and 2nd term which will give you the first term of this sequence which is 1. It is important that the first difference should be one before you start the working because these are second difference sequences. In the first difference type of sequences, they can start with any number. But in these you have to be careful! So whenever you are doing any questions of second difference , always see that any term you have has a first difference of 1!
Having explained that, I will now tell you how to find the nth formula. We know that Nth formula is An= a+(n-1)d
'a' is the first difference of the term. 'd' is the difference of the 2nd and the 1st term.
The working for this is nth term number - (2nd a/2)(nth term)^2 = whatever the answer is.
e.g 1) 1-(0.5)(1)^2 = 0.5
2) 2-(0.5)(2)^2= 0
3) 4-(0.5)(3)^2 = -1/2
d= 2nd term - 1st term or 3rd term - 2nd term
d= -0.5 , a= 1/2
An = a+(n-1)(d)
An= 0.5+(n-1)(-0.5)
An= 1/2+1/2 - 0.5n
An= -1/2
+1Now you have found the nth formula. Add this into the one that I found earlier.
It will be 0.5(n^2)-0.5n+1
The sequence is 1,2,4,7,11,16
Happy day everyone!
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:lol: