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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