[Guest]

I came across this number sequence last week, and although I've come back to it daily, I can't seem to crack the damn thing. What do you think it is? What's the pattern?

9, 16, 25, 36, 49, 14, 31, 0, ?

[Guest]

They squares of numbers (3 to 10)

minus nearest 50xn.

After 49 there is 14 (64-14)

then 31 (81-50) then 0 (100-100)

[bonanova]

Here is an excellent source for finding sequences.

Yours wasn't in it, however.

[Guest]

Hmm! I suspect the user above is right, and clever to get it so fast. Thanks ever so much.

[Guest]

I came across this number sequence last week, and although I've come back to it daily, I can't seem to crack the damn thing. What do you think it is? What's the pattern?

9, 16, 25, 36, 49, 14, 31, 0, ?

they go up in odd numbers, e.g 9+7=16, 16+9=25 etc

[Guest]

they go up in odd numbers, e.g 9+7=16, 16+9=25 etc

When I was younger, I never noticed the pattern of the squares, only that they increased in sequential odd numbers (1-0=1, 4-1=3, 9-4=5, 16-9=7, etc). I used to try and figure out the explanation behind this, and if I remember correctly (it's been since middle school probably), I came up with an equation something along the lines of:

(X+1)^2 - X^2 = 2X - 1

So, if X = 5, you have 6^2 - 5^2 = 9.....36-25=9

I would go and break this down and try to find an explanation, but I have to pay attention to the meeting I'm in now. If anyone can help me out, you'd finally put my mind to rest after 10 years

[Guest]

When I was younger, I never noticed the pattern of the squares, only that they increased in sequential odd numbers (1-0=1, 4-1=3, 9-4=5, 16-9=7, etc). I used to try and figure out the explanation behind this, and if I remember correctly (it's been since middle school probably), I came up with an equation something along the lines of:

(X+1)^2 - X^2 = 2X - 1

So, if X = 5, you have 6^2 - 5^2 = 9.....36-25=9

I would go and break this down and try to find an explanation, but I have to pay attention to the meeting I'm in now. If anyone can help me out, you'd finally put my mind to rest after 10 years

Close, except 36-25=11

(x+1)²-x²=2x+1

x²+2x+1-x²=2x+1

2x+1=2x+1

QED

[Guest]

Yah, simple error because I was sloppy. But yah, my equation works out--I was just curious why those two equations match? And what does QED stand for?

BTW--it can also be written as X^2 - (X-1)^2 = 2X - 1....I think this is where my error may have originated from

And I think the thing that fascinated me most was that the difference was always equal to (X+1) + (X), which in equation form comes out to 2X + 1 [nothing special], but when applied to numbers, using X=4 and (X+1)=5, you get 9. 5^2 - 4^2 = 9 I understand the equations I've come up with shaping this, but WHY do the equations work out this way? What is it about squaring numbers that creates this peculiarity?

4x4 = 4 + 4 + 4 + 4 = 16

5x5 = 5 + 5 + 5 + 5 + 5= 25

So you'll have X occurrences of a difference of 1, plus the additional difference of (X+1). Thus, 4(1) + 1(5) = 9

I think I just figured out the reason why those equations match....sorry for using Brainden as my own personal workspace

[Guest]

HIKE!

[Guest]

Yah, simple error because I was sloppy. But yah, my equation works out--I was just curious why those two equations match? And what does QED stand for?

BTW--it can also be written as X^2 - (X-1)^2 = 2X - 1....I think this is where my error may have originated from

And I think the thing that fascinated me most was that the difference was always equal to (X+1) + (X), which in equation form comes out to 2X + 1 [nothing special], but when applied to numbers, using X=4 and (X+1)=5, you get 9. 5^2 - 4^2 = 9 I understand the equations I've come up with shaping this, but WHY do the equations work out this way? What is it about squaring numbers that creates this peculiarity?

4x4 = 4 + 4 + 4 + 4 = 16

5x5 = 5 + 5 + 5 + 5 + 5= 25

So you'll have X occurrences of a difference of 1, plus the additional difference of (X+1). Thus, 4(1) + 1(5) = 9

I think I just figured out the reason why those equations match....sorry for using Brainden as my own personal workspace

QED is an abbreviation of the Latin phrase "quod erat demonstrandum" (literally, "that which was to be demonstrated"). You put it at the end of a proof to indicate you've proved what you were trying to. I had just demonstrated that(x+1)²-x²=2x+1 by showing it can be reduced to 2x+1=2x+1, which is clearly a true statement. Using "QED" in everyday communication can make you look like a sophisticated intellectual or a pompous jerk, sometimes simultaneously but usually one or the other at a time.

[Guest]

LOL--so a fancy way of saying "TADA!"

Thanks for that--it came up in a crossword puzzle this morning and it bothered me greatly that I couldn't solve it on it's own (fortunately I had the down clues to fill in the word)