[Closed] Maths! nth term help please

Squares

36

n^2 i.e. n*n

The nth term is n^2, the rule is square the number to get the appropriate term (ie, multiply it by itself - 4*4=16, 5*5=25, etc)

So its nsquared?

Indeed it is.

It's the difference between the 2 previous numbers plus 2 then add the last number.

Far easier than a stupid formula.

[quote=Drac said]It's the difference between the 2 previous numbers plus 2 then add the last number.
Far easier than a stupid formula.

What about 1 & 4 where there are no two previous numbers 🙂 ?

What about 1 & 4 where there are no two previous numbers ?

That's your reference point.

Sorry I should add that yours is the answer they'll want that is the square root sequence but I'm showing there's other ways too.

Out of all the maths I've done I don't ever recall doing these sequences? 😳
I'd got the answer but just didn't know the term/rule bits.
Time to dig out the old books I think.

Easier to see it when you set it out like this:
[code]
Where it comes in Sequence (call it N): 1 2 3 4 5
What the value is (call it A): 1 4 9 16 25
list of Ns - 1 2 3 4 5
List of As - 1 4 9 16 25
[/code]
You can see that to get from N to the corresponding A, you just square N. So, A = N²

I feel your pain, same thing here x2!

There is no correct answer. I immediately came up with the same pattern as Drac, which oddly gives the next 3 terms as 36, 49, 64 the same as the n squared pattern. I was always taught not to answer such questions at school. You can induce as many patterns as you like, no one is more correct than any other.

Thats exactly as i saw it scuzz. It was when the daughter started talking about the nth term I was lost.
I did a level maths and then subsequently maths for chemistry at uni.
It does worry me how beer and falling off bikes/scaffold/the ground has dimmed my brain!

No worries, from the formula we could say:
"1st term, N = 1, A = N² = 1² = [b]1[/b]"
"2nd term, N = 2, A = N² = 2² = [b]4[/b]"
"3rd term, N = 3, A = N² = 3² = [b]9[/b]"
But the general formula of A = N² works for [i]any[/i] term, whether it's the 1st, 2nd, 18th or 9,898,781th.
So, we say the formula is for the [i]Nth[/i] term. We then replace N with whatever term it is we want to find.

drac's way is a long winded way of showing that...

x^2 = 2x^2 -4x +2 -x^2 +4x -4 +2

or you could just say...
y=x^2 😉

but then I guess lots of us see an obvious pattern, and others don't

===

remember a similar one in school...

pick a number (eg 5)
multiply it by itself (25)
now take the number each side of the original and multiply them (4x6=24)
isn't it fantastic that the answer is one lower than the original number squared?

everyone trying all kinds of numbers to see if it works. even had one guy write a program to automate it.

or you could save a lot of effort and just write (x-1) * (x+1) = x^2 +x -x -1 😉

Far easier than a stupid formula.

Hmmm...

X(n) = 2X(n-1) - X(n-2) + 2
X(3) = 2.4 - 1 + 2 = 9
X(4) = 2.(2.4 - 1 + 2) - 4 + 2
X(5) = 2.(2.(2.4 - 1 + 2) - 4 + 2) - (2.4 - 1 + 2) +2
etc...

or X(n) = n*n

Now prove by induction that for X(1)=1 and X(2)=4, that X(n) simplifies to n*n

Cheers for proving my point fellas with you complex formulas.