In Exercises 61–68, use the graphs of and to find each indicated ...

Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

Graph showing points for sequence a_n in college algebra, chapter on sequences.

Graph showing points for sequence b_n in college algebra, chapter on sequences.

5Σi=1 (a_i+3b_i)

Accepted Answer

Hello. Today we're going to be using the two given graphs to evaluate the given summation. Now, before we take a look at the summation, let's go ahead and take a look at the two given graphs. The graph on the left shows every term in the sequence A sub N and the graph on the right shows every term in the sequence B sub N. So what we want to go ahead and do is label every point in the given graphs. And the way that we're going to do that is we're going to take a look at every value of N and figure out what the corresponding value to that point is going to be. So for example, in the A sub N graph, when N is equal to one, we get the return value of four. And that means that a sub one is going to equal to positive four. Now what we want to do is repeat this process for every other point in the graph. So when N is equal to two, we get the return value of positive one. So a sub two is equal to one when N is equal to three. We get the return value of negative two. So a sub three is equal to negative two. And finally, when N is equal to four, we get the value of negative five. So a sub four is equal to negative five. Now we want to repeat this process for the B sub N graph. When N is equal to one, we get negative five. So B sub N or I'm sorry, B sub one is going to equal to negative five. When N is equal to two, we get negative two. So B sub two is equal to negative two. When N is equal to three, we get one. So B sub three is equal to positive one. And finally, when N is equal to four, we get positive four. So be sub four is equal to four. Now that we have every point on the graphs labeled, let's go ahead and take a look at the given summation. The given summation states that we want to add the first four terms of five times every term in A plus, every term in B. And the way that's going to look is we're going to take the first term which is when N is equal to one. So that's going to be five times a sub one plus B sub one. Now we know that A sub one is equal to four and B sub one is equal to negative five. So the first term in the summation is going to be five times four plus negative five. And we're going to repeat this process for the next four terms. So the second term is when N is equal to two, that's going to give us five times a sub two, which is one plus B sub two, which is negative two. Then we're going at the term when N is equal to three. So that's going to give us five times a sub three which is negative two plus B sub three, which is positive one. Then finally, we're going to add when N is equal to four and that's going to give us five times A sub four which is negative five Plus B sub four which is positive for. And now we just want to go ahead and simplify In the first term, five times four is going to give us 20. In the second term five times one is going to give us one. In the third term, five times negative two is going to give us negative 10. And in the last term, five times negative five is going to give us negative 25. Now 20 plus negative five is going to give us positive 5 plus negative two is going to give us positive three, negative 10 plus one is going to give us negative nine and negative 25 plus four is going to give us negative 21. So this summation is going to simplify to 15 plus three minus nine minus 21 which is going to give us a final total of negative 12. And that's going to be the evaluated form of the given summation. And with that being said, the answer to this problem is going to be D so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 (a_i+3b_i)

Key Concepts

Sequences

Summation Notation

Graph Interpretation

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