For Exercises 45–50, write out the first three terms and the last...

Question

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

Summation formula for an arithmetic sequence from i=1 to 17 of (5i + 3).

Accepted Answer

Hey everyone in this problem we are asked to identify the first four terms and the last term. And to evaluate the some using the formula given S. N. Is equal to N. Over two times a one plus A. M. And the sum that we're given is I from 1 to 21 of seven I plus two. All right now let's go ahead and start with the first term. Okay when we're talking the first term we're gonna talk about the first I. Value. Okay in this case we have I starting at one given by blue. Okay So we're gonna have I. Is equal to one for our first term. And our terms each of our terms is given by seven I plus two. Okay so we're going to get seven I which is gonna be seven times one plus two Which is equal to nine. Alright. Moving on to the second term. The second term I starts at one and it's just going to increase by one each time. So in the second term we're gonna have I is equal to two we're gonna get seven times I so seven times two plus two Which is equal to 16. In the third term We're gonna get eyes equal to three seven times three plus two. This is gonna be 23. And in the fourth term same thing you can see the pattern here I is equal to 47 times four. Last two Is equal to 30. Okay and you can see we're going up by seven each time. Alright great. We found the first four terms. Let's go ahead and do the last term. Okay. Now, the last term. What's the I gonna be when we get to the last room? Well, that's given at the top of our some here. Okay. So the bottom tells us that I starts at one and then the top tells us it's gonna go all the way until I was 21. Okay. So the last term is going to be given when I is equal to 21, this is going to make our term seven times I. So seven times 21 plus two, Which is equal to 149. All right. We found the first four terms. We found the last term. Now what we want to do is to find the sum using the formula we were given. Okay, Now the formula again, S. N. Is equal to N over two times a one plus A N. Okay, well, and over to our value is going to be this top value when we start up one, it's the number of terms. It's going to be this top value when we start at one. So in this case it's 21. So we have 21/2. A one A plus a 21. No, In this case a one A 1 is our first term. We found our first term which is nine and a 21 is when I is 21 or you can call this the last term. But we know that that's going to be 149. Alright. And working this out, we are going to get 1,659 and that is the sum. All right. So comparing this to the answers, we know that the first term is nine, the second term is 16, the third term is 23. The fourth term is 30. The last term is 149 and the sum is 1,659. We have answer. D Thanks everyone for watching. I hope this video helped see you in the next one.

For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

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