Stock market 2

For the week of July 22, the forecaster recorded the following day-to-day changes in the stock market of a specific stock: -2 on Monday, +4 on Tuesday, -8 on Wednesday, + 2 1/2 on Thursday, - 3 1/4 on Friday. The stock began the week at 78 points. How many points did it finish with at the end of the week?

Correct answer:

a₅ =  71 ¹⁄₄ = 285/4

Step-by-step explanation:

$$\begin{gathered} m_4=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2\frac{1}{2}=2.5 \\ {m}_5=3\frac{1}{4}=3+\frac{1}{4}=\frac{3\cdot 4+1}{4}=\frac{12+1}{4}=\frac{13}{4}=3\frac{1}{4}=3.25 \\ {a}_0=78 \\ {a}_1=a_0-2=78-2=76 \\ {a}_2=a_1+4=76+4=80 \\ {a}_3=a_2-8=80-8=72 \\ {a}_4=a_3+m_4=72+\frac{5}{2}=\frac{72\cdot 2}{2}+\frac{5}{2}=\frac{144}{2}+\frac{5}{2}=\frac{144+5}{2}=\frac{149}{2}=74.5 \\ {a}_5=a_4-m_5=\frac{149}{2}-\frac{13}{4}=\frac{298}{4}-\frac{13}{4}=\frac{298-13}{4}=\frac{285}{4}=71\frac{1}{4}=71.25 \end{gathered}$$

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