Determine the perimeter of the 100th figure in the following pattern.?

Question

Assume that all sides are 1 cm long. Pattern is here:http://img227.imageshack.us/img227/1777/patternux8.png I got 398 cm but my teacher told me that wasn't it. Teach me, please. Thank you.

What's the pattern? I know how the equation for perimeter works I just need to find a way to find the number of squares and the pattern to get there

Answer 1

The correct answer is 2^100 + 2. For each figure, you multiply 2 to the power of the position of that figure and then add 2. For example, the first figure is 2^1 + 2 = 4. The second is 2^2 + 2 = 6. So, the 100th figure should be 2^100 + 2. The actually perimeter is too large to calculate, but is roughly:

1.2676506 x 10^30 cm.

Though, I'm sure your teacher would be satisfied with
2^100 + 2. =)

Answer 2

The left and right sides are always 1 cm. The top and bottom are always equal to n cm, where n is the number of blocks.

So the perimeter for n blocks would be: 2(n+1).
1 block = 2(2) = 4
2 blocks = 2(3) = 6
4 blocks = 2(5) = 10
etc.

First, am I correct in assuming that you have 1 block, then 2 blocks, then 4 blocks, then 8 blocks, then 16 block? It appears to double each time.

That would make a total of 2^100 blocks in the end. Thus the perimeter would be:
2(2^100 + 1) =
2^101 + 2 cm

That's a large number... about 2.5353012 × 10^30 or about.2.5 nonnillion centimeters.

Answer 3

The perimeter is 2 n +2 where n is the number of pieces.
To determine the number of pieces ofthe 100 th piece let look for a serie :
The first has one the second 2 and the third 4
so it can be :
1) 2^n-1 that give 2^99 that is a too big number
633825300114114700748351602688
so perimeter is 2n+2
1267650600228229401496703205378 cm
2) that can be a serie with +1, +2, +3 and following
so the figure 100 will be :the sum of an arithmetical serie with 1 to 100 : the sum is 101* 100/2 = 5050
so the perimeter is 2n+2= 10102 cm

Answer 4

The formula for the perimeter is #blocks * 2 + 2. For example, there are three blocks. There are then three top pieces, three bottom pieces, and an end and a front.

For 100 pieces, the perimeter should be 100*2 + 2 = 202.