Help on a math question...

https://ibb.co/gF4xB7p

I have uploaded the question to imgBB.
Here is my thought process but I am still confused after looking at the mark scheme
1. Set the two sequences equal to each other
2. Move the numbers around until you get n^2 on its own
3. It becomes n becomes + and - because it is rooting
4. Discard the negative as N can't be a negative number

Eventually I got +sqrt(41/3) where I discarded the -sqrt(41/3)
The mark scheme says it's wrong.
Can someone show me some working on how to get the correct answer?

Reply 1

full-size-hustle

bump

Reply 2

DFranklin

Original post by full-size-hustle

https://ibb.co/gF4xB7p
I have uploaded the question to imgBB.
Here is my thought process but I am still confused after looking at the mark scheme
1. Set the two sequences equal to each other
2. Move the numbers around until you get n^2 on its own
3. It becomes n becomes + and - because it is rooting
4. Discard the negative as N can't be a negative number
Eventually I got +sqrt(41/3) where I discarded the -sqrt(41/3)
The mark scheme says it's wrong.
Can someone show me some working on how to get the correct answer?

You can't "set the two sequences equal to each other". Consider the two sequences x_n = n and y_n = n+1. Obviously x_n never equals y_n. But 2 is in both sequences.

In this case, one sequence is obviously increasing and one sequence is obviously decreasing, so the easiest thing is to list the members that are potentially in range of each other and show there are no shared values.

Reply 3

full-size-hustle

Original post by DFranklin

You can't "set the two sequences equal to each other". Consider the two sequences x_n = n and y_n = n+1. Obviously x_n never equals y_n. But 2 is in both sequences.
In this case, one sequence is obviously increasing and one sequence is obviously decreasing, so the easiest thing is to list the members that are potentially in range of each other and show there are no shared values.

Could you please explain what you mean by x_n? is it x-n?
The idea of one increasing and one decreasing makes sense, and I can see why listing the values out would work, thanks. However I am still unsure of the reason why we can't set the two sequences to be each other...

Reply 4

Ajhdhd

Original post by full-size-hustle

https://ibb.co/gF4xB7p
I have uploaded the question to imgBB.
Here is my thought process but I am still confused after looking at the mark scheme
1. Set the two sequences equal to each other
2. Move the numbers around until you get n^2 on its own
3. It becomes n becomes + and - because it is rooting
4. Discard the negative as N can't be a negative number
Eventually I got +sqrt(41/3) where I discarded the -sqrt(41/3)
The mark scheme says it's wrong.
Can someone show me some working on how to get the correct answer?

yes it would seem that from the mark scheme you will have to list out a few values. Once you find the overlap you need to recognise that one is decreasing and one is increasing so they will never overlap again

(edited 11 months ago)

Reply 5

zmp903

Original post by full-size-hustle

https://ibb.co/gF4xB7p
I have uploaded the question to imgBB.
Here is my thought process but I am still confused after looking at the mark scheme
1. Set the two sequences equal to each other
2. Move the numbers around until you get n^2 on its own
3. It becomes n becomes + and - because it is rooting
4. Discard the negative as N can't be a negative number
Eventually I got +sqrt(41/3) where I discarded the -sqrt(41/3)
The mark scheme says it's wrong.
Can someone show me some working on how to get the correct answer?

What i did for this is just to make a table of the values of the sequences at n=0, n=1, n=2...
The sequences move in opposite directions and will never go backwards because n is squared, so the value for n=-1 is the same as n=1. Once it goes past each value's number at n=0 (the lowest/highest the sequence will go, eg -1 for 2n^2-1 or 40 for 40-n^2) you can stop counting since none of those values will be reached by the other number.

n I 0 I 1 I 2 I 3 I 4 I 5 I 6 I 7 I
2n^2 - 1 I -1 I 1 I 7 I 17 I 31 I 49 I..........
40-n^2 I 40 I 39 I 36 I 31 I 24 I 15 I 4 I -9 I.....

We can see the only number that matches is 31.

Reply 6

old_engineer

Original post by full-size-hustle

The number that occurs in both sequences might be the nth member of the first sequence and the mth member of the second sequence. That’s why you can’t just equate the two sequences. What you can do, though is:

2n^2 - 1 = 40 - m^2

If you rearrange that to m^2 + 2n^2 = 41, you should find that there are only a few values of m that you have to try.

Reply 7

DFranklin

Original post by full-size-hustle

x_n is a fairly standard online notation for

x_n

Reply 8

faithfaithhi

Hi, if you use your idea of setting them equal to each other, what you are finding is a not a term's value but the position of a common term. Root 41/3, is 3.69 so the position of the value is 3/4 in each sequence (n must be an integer) so write out but sequences up to the 4th term, you should see that the value in common is 31!