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Norma-Jean [14]
1 year ago
10

A student ran a distance of 3 miles each day for 5 days. Then the student ran a distance of 4 miles each day for the next 5 days

Mathematics
1 answer:
azamat1 year ago
8 0
The total distance was 35 miles. Why? Well, see below:

The student ran 3 miles each day for 5 days. That can be representative of:

Day 1: 3 miles
Day 2: 3 miles
Day 3: 3 miles
Day 4: 3 miles
Day 5: 3 miles

Adding these values together, we will find that the student ran a total of 15 miles in the first five days.

As for the next set of 5 days, we can represent this by modeling like we did above:

Day 6: 4 miles
Day 7: 4 miles
Day 8: 4 miles
Day 9: 4 miles
Day 10: 4 miles

Adding the values from the second set of days, we will find that in days 6-10, the student ran a total of 20 miles.

We can add the total values together to identify the total distance the student ran during these 10 days.

15 + 20 = 35 total miles

Hence, the student ran a total of 35 miles over the course of 10 days. If you need help, let me know and I will go ally assist you.
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Write the first three terms of the series for which tn = 2(n+3). Find the number of terms of the series required to make the sum
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Answer:

The first three terms of the series are 8, 10 and 12. The number of terms is 12 to make the sum 228.

Step-by-step explanation:

The series is defined as

t_n=2(n+3)

Put n=1.

t_1=2(1+3)=2\times 4=8

Put n=2.

t_2=2(2+3)=2\times 5=10

Put n=3.

t_3=2(3+3)=2\times 6=12

The first three terms of the series are 8, 10 and 12.

It is an arithmetic series. The first terms is 8 and the common difference is

d=a_2-a_1=10-8=2

The sum of n terms of an arithmetic series is

S_n=\frac{n}{2}[2a+(n-1)d]

288=\frac{n}{2}[2(8)+(n-1)2]

288=\frac{2n}{2}[8+n-1]

288=n[n+7]

0=n^2+7n-288

0=n^2+19n-12n-288

0=n(n+19)-12(n+19)

0=(n+19)(n-12)

Equate each factor equal to zero.

n=-19,12

The number of terms can not be negative, therefore the value of n must be 12.

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Step-by-step explanation:

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