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Determine the sum of the first 6 terms of the geometric sequence 1,3,9,S6...

Question

Determine the sum of the first 6 terms of the geometric sequence 1,3,9,S6

Determine the sum of the first 6 terms of the geometric sequence 1,3,9, S6



Answers

Find the sum of each geometric series.
$3-6+12-\cdots$ to 7 terms

We're asked to sum this up until you get the six term. So what we're looking for? First of all, we eat a one. A one is 54. We need N and he's six. And then we need to figure out what our is. And our is just 36/54. Really? And if you reduce that by nine, you get four over. But if either moved by nine, you get 4/6, and then that reduces the 2/3. Okay? Or you could just divide the boat by 18. So we get 2/3 of her are so s of six, then is a one which is 54 onto one minus 2/3. That's our the end, which is six and then divided by one minus 2/3. Now, at this point, you can either plug this into your calculator right away or you if your calculator allows you to do that, or you can do it in steps. Um, it's up to you. So I'm gonna do it in steps because my calculator is not going to allow me to do it any more than that. Um, some calculators do, but that's okay. So the first thing I'm gonna do is I'm gonna raise everything to the six power and here secure the 60. 64 36 729. And then down here, I'm gonna actually subtracts. I'm gonna get 1/3 okay? And then I'm going to say that that means this is equal to I jump back here of one minus 64 over 729 is 729. My mint 64 were over 296 165 over 729 and that is divided by 1/3. So that's 54 times 6 65/7 29 then times three, okay, because it's divided by 1/3. And I'm just gonna do that on my calf. It's gonna multiply 54 by 665 by three. And then I'm gonna divided by 729. And it comes over you, um, 147.7, repeating. Or if you want to do it as a fraction, it's gonna come over to 13. 30 over nine. Okay, so either way, it doesn't really matter of which way you express it. That's the answer. So 147.7, repeating or 1330 over nine

All right. Welcome backs for this problem. Um, we're gonna be finding the some the 1st 6 terms of a geometric sequence that is to six. 18. All right, so, uh, they were going to use that. Do this is we're gonna use this, uh, nice little equation right here where we will. Your first term is one minus. The common ratio to be and over one. When is our so well? Let's take a look at this. Our first term is to looks like we got by a factor of three each time. Right? So your family wanted by by three. So are, as he put it, three anyone is going to and we're finding some of the 1st 6 terms. So if we put that in direct reason right here, that's two times one minus r t six divided by one minus, uh three. And that it's just sequitur your 700 Tween

We were given a geometric series that is 1/9 minus 1/3 plus one and then minus dot, dot, dot never asked to find the sum to six terms. So the easiest way to do that? Because we have three terms and we are be no them. And we can notice that we're really just multiplying by three each time and then sign is changing. So we're actually multi 1,000,000 minus three. We can just right of the series to six term that was You can go minus three and then plus nine and then minus 27. Okay, just times in my minus three each time. And then we just add those together. So one night, minus three nines, then plus 9/9 minus 27 overnight is multiplying everything by nine. Here it's 81/9, and then the last one is, uh, 27 times nine Terry. So 243 over nine. And what I'm trying to do then, is just that at the top. So one minus three plus nine, minus 27 plus 81 minus 243. So I get minus 182 over nine upset you. I get my 180 to 189 overnight, and that's my final answer.

According to the question friend of for seven terms Off GP, we have the given sequence is six plus 12 plus 24 plus so on. We know that first awful toe even is six on the value of our is wow upon six degrees Don't And we can say that we find out the 1st 7th it means an is equal to seven. Also given and we know that the formula off some there is a are raised to power and minus one up on R minus one. In that case, when R is greater than is one when we substitute the value here you find out some off seven Tom, it means as salan You're a is six and our is no and is seven miners one a bone. Odd is tu minus one on Soling. We have f seven is equal to the value comes out six to rest of our seven minus one upon one. When the soul for the this the question comes out six in tow 1 27 and the finals that we get someone 62 evil as seven means 1st 7 dome some


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