Fraction

Aim: In this task you entrust consider a set of numbers that be presented in a centrosymmetric pattern. Figure 1 : Lacsaps Fractions The first five rows of numbers are shown above. In order to find the numerator of the sixth row, I will use the numbers that go down the triangle diagonal, as shown from the highlighted fractions above. Hence the numerators are: 1 3 6 10 15 Row Numerator 1st difference 2nd difference 1 1 2 3 3 6 4 10 5 15 Figure 2 : Table masking family relationship between n rows and numerator The table above shows the relationship between row and numerator. The first difference between the numerator in row 1 and 2 was 2, between row 2 and 3 was 3, and so forth (2, 3, 4, 5). The second difference for apiece row number is 1, hence the equation for the numerator is a nonrepresentational sequence. Therefore, the find the equation of the sequence, the quadratic construction, y = ax2 + bx + c should be used, where y is the numerator and x is the row number.

To find this general arguing for the numerator, I will calculate the values of a and b using simultaneous equations (substitution method): Using the values from the table: x = 2 and y = 3 (second row) backing into the quadratic formula (c is disregarded), and make b the subject: 3 = a (2)2 + b(2) + 0 3 = 4a + 2b b = -2a + 1.5 Using the values from the third row : x = 3 and y = 6 6 = a (3)2 + b(3) + 0 6 = 9a + 3b Substitute b = -2a + 1.5, 6 = 9a + 3(-2a + 1.5) 6 = 9a - 6a + 4.5 3a = 1.5 a = 0.5 Therefore, b = -2(0.5) + 1.5 b = -1 + 1.5 = 0.5 We have come to a general stat If you want to desexualize a full essay, order it on our website: Ordercustompaper.com

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