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vitfil [10]
3 years ago
8

Find the first, fourth, and eighth terms of the sequence.

Mathematics
1 answer:
Oksana_A [137]3 years ago
6 0
a(n)=-3\cdot2^{n}-1\\\\a_1=-3\cdot2^1-1=-3\cdot2-1=-6-1=-7\\a_4=-3\cdot2^4-1=-3\cdot16-1=-48-1=-49\\a_8=-3\cdot2^8-1=-3\cdot256-1=-768-1=-769\\\\if\ a(n)=-3\cdot2^{n-1}\ then\\\\a_1=-3\cdot2^{1-1}=-3\cdot2^0=-3\cdot1=-3\\a_4=-3\cdot2^{4-1}=-3\cdot2^3=-3\cdot8=-24\\a_8=-3\cdot2^{8-1}=-3\cdot2^7=-3\cdot128=-384
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Answer:

Then, the object will take 29.11 min to travel 4\frac{9}{10}miles

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When an object is moving at a steady speed, we can calculate the time it would take to travel a given distance using the following formula:

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In this particular, both the given speed and distance are mixed fractions so we'll first convert them into improper fractions to operate more easily:

speed=10\frac{1}{10} \frac{mi}{h} =\frac{(10*10)+1}{10} \frac{mi}{h}=\frac{101}{10}  \frac{mi}{h}

distance=4\frac{9}{10}mi=\frac{(4*10)+9}{10}mi=\frac{49}{10}mi

So, now we can calculate the time using the equation 1:

time=\frac{distance}{speed}=\frac{\frac{49}{10}mi }{\frac{101}{10} \frac{mi}{h} } =\frac{49*10}{101*10} h

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