Eduardo

Eduardo wrote a fraction problem by adding 1/4 and then subtracting 2 1/2 in the same pattern, and he got these numbers: 8 5/8, 6 1/8, 6 3/8, 3 7/8
Identify the next two numbers in the pattern

Final Answer:

a₅ =  4 ¹⁄₈ = 33/8
a₆ =  1 ⁵⁄₈ = 13/8

Step-by-step explanation:

$$\begin{gathered} a_1=8\frac{5}{8}=8+\frac{5}{8}=\frac{8\cdot 8+5}{8}=\frac{64+5}{8}=\frac{69}{8}=8\frac{5}{8}=8.625 \\ {a}_2=6\frac{1}{8}=6+\frac{1}{8}=\frac{6\cdot 8+1}{8}=\frac{48+1}{8}=\frac{49}{8}=6\frac{1}{8}=6.125 \\ z=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2\frac{1}{2}=2.5 \\ w=\frac{1}{4}-z=\frac{1}{4}-\frac{5}{2}=\frac{1}{4}-\frac{10}{4}=\frac{1-10}{4}=\frac{-9}{4}=-\frac{9}{4}=-2\frac{1}{4}=-2.25 \\ {a}_3=a_1+w=\frac{69}{8}+\frac{-9}{4}=\frac{69}{8}+\frac{-18}{8}=\frac{69+(-18)}{8}=\frac{51}{8}=6\frac{3}{8}=6.375 \\ {a}_4=a_2+w=\frac{49}{8}+\frac{-9}{4}=\frac{49}{8}+\frac{-18}{8}=\frac{49+(-18)}{8}=\frac{31}{8}=3\frac{7}{8}=3.875 \\ {a}_5=a_3+w=\frac{51}{8}+\frac{-9}{4}=\frac{51}{8}+\frac{-18}{8}=\frac{51+(-18)}{8}=\frac{33}{8}=4\frac{1}{8}=4.125 \end{gathered}$$

$a_6=a_4+w=\frac{31}{8}+\frac{-9}{4}=\frac{31}{8}+\frac{-18}{8}=\frac{31+(-18)}{8}=\frac{13}{8}=1\frac{5}{8}=1.625$

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