Please please please help me with this. I can't remember how to work this problem out. If someone could explain to me how to do
this problem that would be great.
1 answer:
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Answer:
200
Step-by-step explanation:
We have:
We can rearrange the numbers to obtain:
From the left, we can factor out a negative. So:
In other words, we want to find the sum of all the odd numbers from 1 to 99.
And the sum of all the even numbers from 2 to 100.
Let's do each one individually:
Odd Terms:
We have:
We can use the arithmetic series formula, where:
Where k is the number of terms, a is the first term, and x_k is the last term.
Since it's all the odd numbers between 1 and 99, there are 50 terms.
Our first term is 1 and our last term is 99. So, the sum of all the odd terms are:
Divide the fraction. Add within the parentheses:
Multiply:
So, the sum of all the odd terms is 2500.
Even Terms:
We have:
Again, we can use the above formula.
Our first term is 2, last term is 100. And since it's from 2-100, we have 50 even terms. So:
Divide and add:
Multiply:
We originally had:
Substitute them for their respective sums:
Multiply:
Add:
Multiply:
So, the sum of our sequence is 200.
And we're done!
Note: I just found a <em>way</em> easier way to do this. We have:
Let's group every two terms together. So:
We can see that they each sum to 1:
Since there are 100 terms, we will have 50 pairs, so 50 times 1. So:
Multiply:
Pick which one you want to use! I will suggest this one though...
Edit: Typo
Step-by-step explanation:
If you lost "y" in the first equation.
If first equation is correct.
Answer:
The graph of the data presented is shown in the attached image to this solution.
It shows that the relationship between distance travelled in miles and the time take in hours is D = 55t
Step-by-step explanation:
The distance travelled with the corresponding time taken are presented in the table
Note: D - Distance travelled (miles)
t - Time (hours)
D | t
55 | 1
110 | 2
165 | 3
220 | 4
275 | 5
330 | 6
We are then told to plot these distance travelled on a graph with the time taken.
The distance travelled is plotted on the y-axis and the time in hours is plotted on the x-axis.
The image of the graph of this function will be attached to this answer
It is evident that the graph shows the relationship between the distance travelled and time taken to be D = 55t
Hope this Helps!!!
