Seriously hard Math Help?

Question

Ok we had a problem do day seeling with the pattern 1 3 6 10 15 21 28 36 45 so on and so forth how they ar layers on a block tower first layer 1 block 2nd 3 3rd 6 i hope you get it at this point. This is a quatratic pattern i need and equation where u could tell how many blocks are on any layer like how many blocks are on the 39889 layer i need an eqution to figure this out

Answer 1

The pattern is:
1= 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
and
1 + 2 + ... + n = ?
To answer this last question, let's use an old
trick that Gauss discovered when he was 10 years old.

Note that
1 + n = n + 1
2 + n-1 = n + 1
3 + n-2 = n + 1
.................................
n + 1 = n + 1

Now add the columns. Call the sum we want S
Then S + S = n(n+1)
So S = n(n+1)/2
The number of blocks on layer 39889 is
39889*39890/2

Answer 2

If you know that this is quadratic, then the first is 1, the second is 3, the third is 6, and so on. Those three are enough for now, as are any three.

The equation is y = ax^2 + bx + c, where x is the layer number (1st, 2nd, 3rd, etc.) and y is the number of blocks on that layer. Copy that equation three times, with 1 for x the first time, and the value of y at the time (1 in this case) for y; then repeat with 2 for x and 3 for y, and similarly for the third time.

You will now have a system of equations in three unknowns (a, b and c). Solve that system. Thus:

6 = a*9 + b*3 + c

for the third line, as an example.

Answer 3

The pattern goes like this:
1 + 2 + 3 + 4 + 5
1 + 2 = 3 + 3 = 6 + 4 = 10 etc.

An equation would be...
Let y = the number in the pattern
Let x = the value of the number

y x
1 1
2 3
3 6
4 10
5 15

y = sigma(x_i + x_(i-1) + x_(i-2) + ... + x_1)

I'm not sure if that's what you want or not, but I believe that that is the only way to really represent the pattern.

Answer 4

man my kid and i got that one sorry its 1,2,3,4,5,6,7,8,9 ok??