The bottom row is growing by two (arithmetic sequence) by the time it gets to case 100 the bottom row will have 3 + 2(100-1) objects, which is 201.

This means that in case 100 the rows should follow the following pattern beginning with the first row all the way up to the last row: (1 +3 +...+201)

To figure out the summation one can use the formula (n(a1+an))/2

But first,

To figure out n: 201=1 +2(n-1) n=101 So the sum would be (101(1+201))/2 10,201

For detailed explanations on arithmetic sequences and the formulas check out this website:

http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm