I can't figure out this nth term problem.

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.

Reply 1

Alexion

17

Original post by 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.

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 n², so draw out a table of n² and the values, and see if you can spot a relationship between them.

Reply 2

george1990_

OP

2

Original post by 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 n², so draw out a table of n² and the values, and see if you can spot a relationship between them.

Thanks for the reply!

n^2 = 0,1,2,3,4
Difference/Sequence = +1 (to get to the next number)

:smile:

Reply 3

Ishan_2000

18

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

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Reply 4

wiseCrack

1

Original post by 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.

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

f(n) = n^2 - n

try it

Reply 5

george1990_

OP

2

Original post by wiseCrack

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

f(n) = n^2 - n

try it

Thanks for the reply, but what is f?

Reply 6

Alexion

17

Original post by george1990_

Thanks for the reply, but what is f?

f(n) just means 'a function of n'

Reply 7

george1990_

OP

2

Original post by 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

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