# I can't figure out this nth term problem.

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Hey,

I can't figure out this nth term problem, here is the question:

Every answer I get, whether I used second differences, squaring n or using a table seems not to fit the sequence.

I would be grateful if someone could explain how to work this out to me.

Thanks in advance,

George.

I can't figure out this nth term problem, here is the question:

*Here are the first 5 terms of a quadratic sequence.**1, 3, 7, 13, 21**Find an expression, in terms of n for the nth term of this quadratic sequence.*Every answer I get, whether I used second differences, squaring n or using a table seems not to fit the sequence.

I would be grateful if someone could explain how to work this out to me.

Thanks in advance,

George.

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#2

(Original post by

Hey,

I can't figure out this nth term problem, here is the question:

Every answer I get, whether I used second differences, squaring n or using a table seems not to fit the sequence.

I would be grateful if someone could explain how to work this out to me.

Thanks in advance,

George.

**george1990_**)Hey,

I can't figure out this nth term problem, here is the question:

*Here are the first 5 terms of a quadratic sequence.**1, 3, 7, 13, 21**Find an expression, in terms of n for the nth term of this quadratic sequence.*Every answer I get, whether I used second differences, squaring n or using a table seems not to fit the sequence.

I would be grateful if someone could explain how to work this out to me.

Thanks in advance,

George.

First hint: you're on the right track by using n

^{2}, so draw out a table of n

^{2}and the values, and see if you can spot a relationship between them.

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(Original post by

I can see the nth term formula here, so I'm gonna try to help you find your way to it.

First hint: you're on the right track by using n

**Alexion**)I can see the nth term formula here, so I'm gonna try to help you find your way to it.

First hint: you're on the right track by using n

^{2}, so draw out a table of n^{2}and the values, and see if you can spot a relationship between them.n^2 = 0,1,2,3,4

Difference/Sequence = +1 (to get to the next number)

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#4

The answer is n^2-n+1

The second difference of the original sequence is halved to obtain the coefficient of n^2, which is 1 in this case.

So, write out the sequence for n^2, which should give you:

1, 4, 9, 16, 25

Then write out the original sequence above this. Take the differences between each part of the sequence, so 1-1, 3-4, 7-9, 13-16, 21-25.

Thus, 0, - 1, - 2, - 3, - 4

The nth term of this sequence forms your next part of your answer.

Therefore, the common difference between each part of this sequence is - 1, since this is the first difference, the nth term will be - n.

Write out the sequence for - n.

Take the differences of the sequence of - n from the difference sequence obtained before which was 0, - 1, - 2, - 3, - 4.

This should leave you with the common difference of +1.

Which means the second part of your answer is -n+1.

The whole answer is therefore n^2-n+1

Posted from TSR Mobile

The second difference of the original sequence is halved to obtain the coefficient of n^2, which is 1 in this case.

So, write out the sequence for n^2, which should give you:

1, 4, 9, 16, 25

Then write out the original sequence above this. Take the differences between each part of the sequence, so 1-1, 3-4, 7-9, 13-16, 21-25.

Thus, 0, - 1, - 2, - 3, - 4

The nth term of this sequence forms your next part of your answer.

Therefore, the common difference between each part of this sequence is - 1, since this is the first difference, the nth term will be - n.

Write out the sequence for - n.

Take the differences of the sequence of - n from the difference sequence obtained before which was 0, - 1, - 2, - 3, - 4.

This should leave you with the common difference of +1.

Which means the second part of your answer is -n+1.

The whole answer is therefore n^2-n+1

Posted from TSR Mobile

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#5

**george1990_**)

Hey,

I can't figure out this nth term problem, here is the question:

*Here are the first 5 terms of a quadratic sequence.*

*1, 3, 7, 13, 21*

*Find an expression, in terms of n for the nth term of this quadratic sequence.*

Every answer I get, whether I used second differences, squaring n or using a table seems not to fit the sequence.

I would be grateful if someone could explain how to work this out to me.

Thanks in advance,

George.

f(n) = n^2 - n

try it

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(Original post by

I just read it for 4 minutes but i think the expression is:

f(n) = n^2 - n

try it

**wiseCrack**)I just read it for 4 minutes but i think the expression is:

f(n) = n^2 - n

try it

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#7

(Original post by

Thanks for the reply, but what is f?

**george1990_**)Thanks for the reply, but what is f?

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(Original post by

The answer is n^2-n+1

The second difference of the original sequence is halved to obtain the coefficient of n^2, which is 1 in this case.

So, write out the sequence for n^2, which should give you:

1, 4, 9, 16, 25

Then write out the original sequence above this. Take the differences between each part of the sequence, so 1-1, 3-4, 7-9, 13-16, 21-25.

Thus, 0, - 1, - 2, - 3, - 4

The nth term of this sequence forms your next part of your answer.

Therefore, the common difference between each part of this sequence is - 1, since this is the first difference, the nth term will be - n.

Write out the sequence for - n.

Take the differences of the sequence of - n from the difference sequence obtained before which was 0, - 1, - 2, - 3, - 4.

This should leave you with the common difference of +1.

Which means the second part of your answer is -n+1.

The whole answer is therefore n^2-n+1

Posted from TSR Mobile

**Ishan_2000**)The answer is n^2-n+1

The second difference of the original sequence is halved to obtain the coefficient of n^2, which is 1 in this case.

So, write out the sequence for n^2, which should give you:

1, 4, 9, 16, 25

Then write out the original sequence above this. Take the differences between each part of the sequence, so 1-1, 3-4, 7-9, 13-16, 21-25.

Thus, 0, - 1, - 2, - 3, - 4

The nth term of this sequence forms your next part of your answer.

Therefore, the common difference between each part of this sequence is - 1, since this is the first difference, the nth term will be - n.

Write out the sequence for - n.

Take the differences of the sequence of - n from the difference sequence obtained before which was 0, - 1, - 2, - 3, - 4.

This should leave you with the common difference of +1.

Which means the second part of your answer is -n+1.

The whole answer is therefore n^2-n+1

Posted from TSR Mobile

I've just managed to get my head round that answer!

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#10

(Original post by

Thanks for the reply, but what is f?

**george1990_**)Thanks for the reply, but what is f?

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#12

(Original post by

Please don't post full solutions - it's against forum guidelines

**davros**)Please don't post full solutions - it's against forum guidelines

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#13

(Original post by

Oh right, didn't know that. Sorry.

**Ishan_2000**)Oh right, didn't know that. Sorry.

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