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RideAnS [48]
3 years ago
14

17) Evaluate D(4) Please help

Mathematics
1 answer:
WINSTONCH [101]3 years ago
3 0

Answer:

D(4) = 6

Step-by-step explanation:

Using the blue graph, find the y value when x =4

the y value is 6 when x=4

D(4) = 6

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If S denotes the sum of the first n terms of a geometric series with first term a and common ratio r, then

S=a+ar+ar^2+\cdots+ar^{n-3}+ar^{n-2}+ar^{n-1}
rS=ar+ar^2+ar^3+\cdots+ar^{n-2}+ar^{n-1}+ar^n
\implies S-rS=a+(ar-ar)+(ar^2-ar^2)+\cdots+(ar^{n-1}-ar^{n-1})-ar^n
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Using summation notation, you have

S=\displaystyle\sum_{x=1}^nar^{x-1}=\sum_{x=0}^{n-1}ar^x=a\dfrac{1-r^n}{1-r}

In this case, you have a=2, r=\dfrac12, and n=16. So the value of the sum is

\displaystyle\sum_{x=0}^{15}2\left(\frac14\right)^x=2\dfrac{1-\left(\frac14\right)^{16}}{1-\frac14}\approx2.67

Rounded to the nearest whole number, the answer would be 3.
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3 years ago
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