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1 answer:
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Answer:
1. Juan's marathon training schedule is an example of a geometric sequence
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
3. Lizzy will be better prepared for the marathon
Step-by-step explanation:
In the arithmetic sequence there is a common difference between each two consecutive terms
In the geometric sequence there is a common ratio between each two consecutive terms
Juan's Schedule
∵ Juan's will run one mile on the first day of the week
∴ = 1
∵ He will double the amount he runs each day for the next
6 days
- That means he multiplies each day by 2 to find how many miles
he will run next day
∴ = 1 × 2 = 2 miles
∴ = 2 × 2 = 4 miles
∴ = 4 × 2 = 8 miles
∴ = 8 × 2 = 16 miles
∴ = 16 × 2 = 32 miles
∴ = 32 × 2 = 64 miles
That means there is a common ratio 2 between each two consecutive days
1. Juan's marathon training schedule is an example of a geometric sequence
Lizzy's Schedule
∵ Lizzy's will run 10 miles on the first day of the week
∴ = 10
∵ She will increase the amount she runs by 3 miles each day for
the next six days
- That means she adds each day by 3 to find how many miles
she will run next day
∴ = 10 + 3 = 13 miles
∴ = 13 + 3 = 16 miles
∴ = 16 + 3 = 19 miles
∴ = 19 + 3 = 22 miles
∴ = 22 + 3 = 25 miles
∴ = 25 × 3 = 28 miles
That means there is a common difference 3 between each two consecutive days
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
The rule of the sum of nth term in the geometric sequence is
∵ = 1 , r = 2 and n = 7
∴
∴ = 127
∴ Juan will run 127 miles in the final week
The rule of the sum of nth term in the arithmetic sequence is
∵ n = 7, = 10 and
= 28
∴
∴ = 133
∴ Lizzy will run 133 miles in the final week
∵ 133 miles > 127 miles
∴ Lizzy will run more miles than Juan
3. Lizzy will be better prepared for the marathon
Answer: and
Step-by-step explanation:
For this exercise it is important to remember that Whole numbers Set contains the positive numbers and zero with no fractional part and with no decimal part.
Rational numbers are those numbers that can be written as a fraction, in this form:
Where "a" is the numerator and "b" is the denominator. Both are integers.
Then, given the following fraction:
You can express it as a decimal number by dividing the numerator 31 by the denominator 5:
Based on the definition of Whole numbers, you can identify that:
So the given fraction lies between the following Whole numbers:
and