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OoolMovineJfother question %ll save this respense,Ouesion0l 14Question 11pointLVcLnacrConsioertne folloxing sequence;8.3 X3 =0, X1 =Calculate the general tormula of...

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OoolMovineJfother question %ll save this respense,Ouesion0l 14Question 11pointLVcLnacrConsioertne folloxing sequence;8.3 X3 =0, X1 =Calculate the general tormula of thls sequence Whatts the Value 0i *ado Dot unevaluated expressions Idon t use I2/4-1Mse doreate nacons Gine decima polnts (dont use 1/2,use 0.51 donoukensn Aoccnotatonido Notse 1,234 1.2341

oool Movine Jfother question %ll save this respense, Ouesion 0l 14 Question 11 point LVcLnacr Consioertne folloxing sequence; 8.3 X3 = 0, X1 = Calculate the general tormula of thls sequence Whatts the Value 0i *a do Dot unevaluated expressions Idon t use I2/4-1Mse doreate nacons Gine decima polnts (dont use 1/2,use 0.51 donoukensn Aoccnotatonido Notse 1,234 1.2341



Answers

$$\text { In Problems } 23-28, \text { find the indicated term in each arithmetic sequence.}$$ $$80 \text { th term of }-1,1,3, \dots$$

We are going to do problem number 25. This question we have to find the ends term of the sequence. One managed to uh minus five to find the 90th term of the sequence. So, and its term is a plus and management into the So if we have the first time, that is one, so one plus and management into the D. S. Ministry. The difference between these two is -3. So common differences. Ministry Ministry. So from here and it's time will be coming. There is one man is three and plus three. So here the next jump is four Ministry. So for 90th term, This will be four minutes 3 into 90. So this is four 270. That is a consumer -266. So this is the NFL. That's all. Thank you.

Hello and welcome. We are looking at Chapter two, Section one Problem 55. Now we're given a new type of equation. Well, new to me, maybe not new to you. The Ricker equation. It looks like this. The general form at least. All right, so we're just introducing an exponential. Really? This is be here and were given some parameters values to plug in here, this specific case. So this is what specific to this question here we are asked to plot some terms to see how it behaves. And then kind of in further convergence, Convergence s O. I did use a spreadsheet to graft this. And so, uh, it looks like this. Ah, sequence is converging. Thio this decimal value here Something to do. 0.6931 The last six terms here are all 6.6931 So it's getting closer and closer to some value. This 0.6931 fish. Um, so you can say this appears to converge? We're not sure exactly. Toe what? It's just near 0.6931 All right. Uh, so moving forward from there. It says if so, if it appears to be convergent, estimate the limit and then assuming the limit exists, that is its exact value. So we're gonna estimate 0.6931 and we're gonna assume the limit exists. So just like we've done with a few different problems here, we're gonna make an assumption if we assume the limit exists, we're assuming that the limit as C goes to infinity of except e converges to some value. We're assuming the limit exists. So it goes to l just call it hell. And if we make that assumption that it follows logically that this also except E plus one the next term, uh, the limit as to goes to infinity of that same sequence, basically just one term down the line, it's gonna obviously converge to the same value. All right, So what we do then, is we take the limit of both sides of our equation so I could plug in my see value of two, plug everything in. I'm taking the limit as he goes to infinity of both sides. So the left hand side is definitely getting go to l. That was part of my assumption. My right hand side, it's going to, um Well, I cannot hold the two out of the limit on the right hand side is a little bit more complicated, so let's focus on that first. Yeah. So let's continue this on. Ah, the next page here. So I can sure the work more clearly. All right. So, uh, limits using properties of limits, they're pretty flexible things. Um, So I can write this as the limit s t goes to infinity of except E. And then the limit of a product, you can take the limit of each of the factors. That's one of our linen properties. So by our assumption, we have l equals two. And then this here goes to el by our assumption. And then what weaken do, uh, with this limit here, we can actually move. The limit is just and a constant value 2.7 something so I can actually move the limit into the exponents. That's one of our limit properties as well. So little squished here, but, um, the the limit is in the exponents with the negative x two x sub d. So, after we done resulting all of the limits, it just looks like this. L equals two times at all times E to the negative, Al. So remembering what we know about negative exponents this we could also write this. I would suggest it is running this times one over easy bl or that's the same is over e to be out. So if I want to get, um, l by itself, you could cross, multiply, could do different things. We just want, um, everything in the new greater so I'll go ahead and do it and more steps than I need to. Just to be clear, I just multiply e the lt other side. Now I'm gonna divide both sides by l get you to the l equals two. And then to get rid of that e the exponential I need to use natural logs or natural log cancels with E. If I do it to one side, I have to do it to both sides. And so then I end up with l equals natural law of two s o weaken. Check to see if this works with our our graph by typing in natural log of two into our calculator. If you type in natural, log on to that's what it's approximately 0.6931 So, this, um, this is consistent with our graph. I'll just show you that one more time. This is about 0.6931 from our grasp. All right, so, uh, double checking the question, make sure we answer the whole thing. Um, if it seems to be convergent, estimate the limit. Assuming Dylan just calculate its exact value. And that's exactly what we did. We are.

We are going to do problem number 26. The question is we have to find the 80th term of the sequence. two, comma 5 x two, comma three, comma 7 x two. If they find the difference between these two, then the difference is of one x 2. So the term of the seconds will be a plus And -1 in two d. So putting the value is two plus And management and today is one x 2. So the next time will be two plus And by two minutes. 1 x two. So that's coming out today, it is coming out to be administrator, this is three by two minutes. And by two this is plus any by two, three by two plus and by two. So for eight year term We have to put any equals to 80. So this will be three x 2 plus 80 x two. So this becomes 83 x two. So 80th term of the sequence is 83 x two. This is the answer. Thank you.

We're going to do problem number 27 in this question. But we need to do is we need to find the 80th term for the sequence to Come on. five x 2 comma three 07 x two. So here the difference is fight by to manage to So this is five by to manage two years to five men is four. So this is one by two. Is that common difference? And its term will be for this sequence and the term will be a plus and -1 injury and Venezuelan today, so is two plus And -1 and there is one x 2. So this will be equals to two plus And by two men is one x 2. So this will be equals two To management by two. That is three x 2. Three by two plus n by two. So this is the end it's trump. So for 80th term we have to put any equals to 80. So this will be three by two plus 80 by two. That is 40. So here we are going to get eight year term, There is equals two two. This is three plus 80 so this is 83 by two. This is uh the answer in this case, That's all. Thank you.


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