### 24 Responses

1. john says:

when i first saw this i thought that i was never going to understand it since im hopeless at maths.
but really , this site is great and i really do understand quadratic equations now !!

Like or Dislike: 14  9

2. mking says:

but what if there is more than one nth term

Like or Dislike: 7  8

3. Hey,
Thanks for the article! Very helpful!
I was wondering what level this work is? And is there another quadratic sequence where you have to find a b and c?
Thanks,
Lucie Mcroosy

Like or Dislike: 4  5

• Author says:

Hello Lucie,

This level is what 18-19 would probably do. It is college level maths or equivalent to A level.

I didn’t quite understand your last question.

Like or Dislike: 3  5

• Jason says:

This is for 18-19 years old students
wow,-i’ve fairly recently started year 8 and we’re learning this- i came here for help with my homework i had to find the nth term of two quadratic sequences
1))0,5,12,21,32-Which i think the answer is n2+2n-3
2)0,3,10,19,36
I’m having a lot of trouble with Q.2

Like or Dislike: 2  3

• Jason says:

sorry
just ignore my last comment ive read on

Like or Dislike: 2  4

• Author says:

Hello Jason,

Yes the first one is correct:
$n^2 + 2n -3$
Are you sure you have written the second sequence correctly?

May be the sequence is:
$0, 3, 10, 21, 36$
So then you will get;
$2n^2 – 3n + 1$
I thought I add the answer for you as well since you have spent a lot of time on it.

Like or Dislike: 1  4

4. Hello Author,

Thanks ever so much,
Lucie Mcroosy.

Like or Dislike: 1  3

5. Jon says:

This is only level 7/8 maths at best. That is equivalent to C/B grade at GCSE. However, you would need to have something that includes a more complicated equation so that you could find “b” as well as “c” for the formula. I’ve just taught this to my year 8’s (12 year olds) but they are top set.

Like or Dislike: 5  3

6. Author says:

Your answer is better. I wasn’t sure this was in GCSE and 12 years old exams.

Like or Dislike: 0  4

7. Hey there Mr Jon
Well, I am 12 and second to top set. Top set does level 8, second does level 7. There are 6 sets altogether. We’ve learnt about the a b c. I think ‘a’ its a half the answer from the differences of the differences. ‘C’ is find the 0 term number. And I think ‘b’ is the hardest one-i think you have to do some simplifying and replacing the N’s with term number 1?
Am I wrong? I’ve kinda forgotten.
Lucie Mcroocy

Like or Dislike: 1  3

8. Anonymous says:

Hi, What is the second difference is a constant but it is -5. for example,

Terms 4, -1, -11, -26, -46
Difference -5, -10, -15, -20
2nd Diff -5, -5, -5

How would N to the power of 2 come into this? Help. thanks.

Like or Dislike: 0  3

• Author says:

Hi,

There are no examples of how to handle such a situation.

The nth term is: ½(-5n² + 5n + 8)

Like or Dislike: 0  3

9. Kaitlin says:

I really don’t understand why the n^ thing changes depending on the number? i’ve got online maths homework to do and i have to get over 80% and im just so confused:(((( This helped me a bit but im still so confused

Like or Dislike: 1  2

10. mxxxxxxxxx says:

link to a good online calculator for this??

Like or Dislike: 3  2

11. chasm says:

the question is
12 , 25 , 42 , 63 , 88
can u pls help me find the sequence ?

Like or Dislike: 0  2

• Author says:

Hello Chasm,

You must show that you have tried so that we know where you’re stuck. Have you tried it? So you will need to find the first difference. You do that by subtracting the previous term from the next term. For example:
$25-12=13, 42-25=17, 63-42=21, 88-63=25$
So now you know that the first difference is:
$13, 17, 21, 25$
Using the examples above, I am sure you can continue from here.

Like or Dislike: 1  2

12. *** says:

Hi, what about the sequence : 3,10,21,36,55 ?

Like or Dislike: 0  2

• Author says:

Hi,

You must show that you tried. Start by finding the first difference. Have you tried that?

Like or Dislike: 0  2

13. Reliable says:

Hi!

The example that you’ve shown is to find the nth term of nonlinear sequence with positive second difference. How about sequence with negative second difference? Like this………..

Terms: 36, 35, 32, 27, 20, 11
Difference: -1, -3, -5, -7, -9
2nd difference: -5, -5, -5, -5

How to find?

Like or Dislike: 0  1

14. Helena says:

Hi,
I have this sequence: 2.7,15,26..
The second difference is 3 and I’m not sure what to do?!

Like or Dislike: 0  1

15. Veeti Kuivalainen says:

I have worked on this equation for the past hour.
9,13,13,9,-11,-27,-47
I am in Grade 9 High Level IGCSE Maths, and I can’t do this equation. I know the second difference is -4, and so according to Un=an^2+bn+c, a should be -2. But I can’t figure out b or c; a+b is supposed to be 4 (the first difference) and a+b+c should be 9 (the first term) and so b SHOULD be 6 and c SHOULD be 5 but it simply doesn’t seem to match up to the equation. I really have tried this all, but it isn’t working. PLEASE HELP! Our teacher likes to challenge us, and I’ve done the rest of the homework but this one has got me completely stuck.

Like or Dislike: 0  1

16. ELMA JOPIA says:

There is another way to solve this quadratic sequence faster and easier.

Like or Dislike: 0  1

17. hannah says:

hi whats the nth term of -1, 3, 11, 23, 39? i have tried but cant work it out?

Like or Dislike: 0  1