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

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#1
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.

George.
0
5 years ago
#2
(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.

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.
1
#3
(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.

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

0
5 years ago
#4

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

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.

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

Posted from TSR Mobile
2
5 years ago
#5
(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.

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

f(n) = n^2 - n

try it
0
#6
(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?
0
5 years ago
#7
(Original post by george1990_)
Thanks for the reply, but what is f?
f(n) just means 'a function of n'
0
#8
(Original post by Ishan_2000)

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

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.

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

Posted from TSR Mobile
Thanks! You're a lifesaver!

0
#9
Thanks to everyone who posted for the help!
0
5 years ago
#10
(Original post by george1990_)
Thanks for the reply, but what is f?
f is short for "function of:" and n is short for "number" in this case the number in the series which are 1, 2, 3, 4 and 5
0
5 years ago
#11
(Original post by Ishan_2000)

(stuff)

Posted from TSR Mobile
Please don't post full solutions - it's against forum guidelines
0
5 years ago
#12
(Original post by davros)
Please don't post full solutions - it's against forum guidelines
Oh right, didn't know that. Sorry.
0
5 years ago
#13
(Original post by Ishan_2000)
Oh right, didn't know that. Sorry.
No problem - there's a sticky post near the top of the Maths forum with Guidelines for Posting if you want to have a quick scan through!
0
2 years ago
#14
[QUOTE=george1990_;59506899]Hey,

Answer is n squared + n + 1
0
2 years ago
#15
what is the nth term in this sequence 2,9,18,29,42
0
2 weeks ago
#16
i just had this question too
it directed me on TSR
0
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