This assignment requires us to solve patterns in numerators and denominators in LACSAP’S FRACTIONS, and the first five rows look like:
Figure 1: Lacsap’s Fractions
1 1st row
1 3/2 1 2nd row
1 6/4 6/4 1 3rd row
1 10/7 10/6 10/7 1 4th row
1 15/11 15/9 15/9 15/11 1 5th row Then, let’s look at each part of the question.
Part 1: Numerator of the Sixth Row
Describe how to find the numerator of the sixth row.
For the first part of the question, we need to describe how to find the numerator of the sixth row. To begin with, let’s make all the numerators look the same in a row:
Figure 2: Lacsap’s Fractions
1/1 1/1 1st row
3/3 3/2 3/3 2nd row
6/6 6/4 6/4 6/6 3rd row
10/10 10/7 10/6 10/7 10/10 4th row
15/15 15/11 15/9 15/9 15/11 15/15 5th row Then, we can take out the denominator and go down by the row and just look at the numerator for this part of question, which will look like:
t1=1; t2=3; t3=6; t4=10; t5=15
We can investigate that the numerator starts with 1 in the first row, and the numerators are the same in one row. Each numerator after 1 is the sum of 1+2+…+n (n=row number) which forms an arithmetic series. For example:
When n=3, the numerator will be t3=1+2+3=6.
Table 1: Row Number and Numerator
Therefore, according to this arithmetic series tn=1+2+3+…+n, (n=row number), we can find out the numerator of the sixth row is t6=1+2+3+4+5+6=21
Part 2: General Statement for Numerator and Row Number
Using technology, plot the relation between the row number, n, and the numerator in each...