Sequences and series
1 answer:
<h3>Answer: D) Geometric; r = 4</h3>
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Explanation:
The sequence is not arithmetic because the distance between adjacent terms keeps increasing. For instance, the gap from 0.4 to 1.6 is 1.6-0.4 = 1.2, while the gap from 1.6 to 6.4 is 6.4-1.6 = 4.8. There is no common difference, so we can rule out choices A and B.
To check if we have a geometric sequence, divide each term by its previous term
(term2)/(term1) = (1.6)/(0.4) = 4
(term3)/(term2) = (6.4)/(1.6) = 4
(term4)/(term3) = (25.6)/(6.4) = 4
Each time we get 4 as a result, so this sequence is geometric and the common ratio is r = 4.
Put another way: each new term is found by multiplying the previous term by 4.
0.4*4 = 1.6
1.6*4 = 6.4
6.4*4 = 25.6
This all leads to D being the answer.
Side note: the nth term of this geometric sequence is where n is a positive integer and starts at n = 1.
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Answer:
His average speed on the second day is 35 miles per hour.
Step-by-step explanation:
Consider the provided information.
On first day, he drove 2 hours longer than he drove on second day.
Let x = Number of hours he drove on second day.
Then x + 2 = Number of hours he drove on first day.
It is given that he drove a total of 18 hours.
Therefore,
He drove 8 hours on second day.
x + 2 = 8+2=10
He drove 10 hours on first day.
Let y = speed driven on second day.
y + 5 = speed driven on first day.
As we know: Distance = speed × time
On first day he covers a distance of:
Distance = 10(y+5)
On second day he covers a distance of:
Distance = 8(y)
Total distance = Day 1 distance + Day 2 distance
Hence, his average speed on the second day is 35 miles per hour.