1. Hi all&#33; I got a homework problem that says "it would be more preferable to do it with other people" so could everyone here help me? please? My parents are busy nad they don&#39;t anything bout math.

The Penny Problem

Task 1: This is a image pattern. The first diagram has 1 circle. The second diagram has 5 circles. The third diagram has 12 circles. How many are in fourth? How many circles are in the next three diagrams?

the diagram she supplied us with so I don&#39;t think it&#39;s +6 but i&#39;m not sure.

Task 2: Is there a pattern to the number of circles you added each time? Make a list of all the patterns you notice.

Task 3: in math we want to generalize. Which means predict how the pattern continues. See if you can make a formula to the pattern.

2. me too

3. I realized most of this is rambling, so if you dont bother to look through it my equation was Tn = 1.5(n^2) - 0.5n

Recursive:
T1 = 1
Tn = (Tn-1)-2+3n
T2 = 1-2+3(2) = 5
T3 = 5-2+3(3) = 12
T4 = 12-2+3(4)= 22
T5 = 22-2+3(5)= 35 hmmmmmmmm
Explicit:
Tn = T1 * r^(n-1) <----- i think thats right but i dunno how the hell to us it, so i made this up grrrrr

I found this by looking at the pattern
T2 = 2^2 + 2*.5
T3 = 3^2 + 3*1
T4 = 3^2 + 4*1.5.....
Tn = n^2+1.5n(n-1)
simplifies to.....
Tn = 1.5(n^2) - 0.5n
which works
T1 = 1.5(1*1)-0.5(1) = 1
T2 = 1.5(2*2)-0.5(2) = 5
T3 = 1.5(3*3)-0.5(3) = 12
T4 = 1.5(4*4)-0.5(4) = 22
So you could use that if you wanted to find the nth term, like how many would be in the 100th thingy would be
T100 = 1.5(100*100)-0.5(100) = 9950
Im doing this stuff in math right now, i dunno what i did wrong with the explicit thing grrrr

Its past what your doing, but its one way you could get a formula for it im tired right now be back later

4. Wow&#39;s my math teacher would liek you but I don&#39;t think I should put a formula down since you don&#39;t have to make a formula you just need to find lots of patterns n&#39; such and i wouldn&#39;t be smart enough to think of that

5. What grade/class are you in keikan?

6. math 10 pure but I&#39;m in grade 9 but i&#39;m going to try cuz i got something good going

7. Ok Keikan,
Let&#39;s solve this in a graphical way, as the problem was presented in a graphical way.

At A you see the 4th image

At B I have changed the positions just a little bit.

At C we split off the largest possible square. Amount = I^2

What rests is a triangle with a side always 1 less than the square&#39;s side

At D I added the purple row, and a triangle of the same size.
Now this amount is equal to our first square.

So what is the amount in the triangle?
((I^2)-I)/2

=========> amount in the total image = (I^2)+((I^2)-I)/2

I hope this helps.
Many problems can be solved in a graphical way. Try to understand what I did.

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