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Find the sum of the first 20 terms of the sequence 1, 11,21, 31.S20Enter your answer in the answer box:Beverfor Later...

Question

Find the sum of the first 20 terms of the sequence 1, 11,21, 31.S20Enter your answer in the answer box:Beverfor Later

Find the sum of the first 20 terms of the sequence 1, 11,21, 31. S20 Enter your answer in the answer box: Beverfor Later



Answers

Find the sum of the first 20 terms of the arithmetic sequence: $4,10,16,22, \ldots$

We are given on arithmetic sequence four, then 16 22 and so on, which means the first time is equal to four. On the common Difference Day is equal to a two minus a one, which is equal to 10 minus four, which is equal to six. We know that this summer fend terms often arithmetic sequence has given us in divided by two multiplied with a one plus a n where n is the end. It's tome now, since we have to find the summer 1st 20 terms, which means as 20 will be equal to 20 divided by two multiplied with a one plus 8 20 now 8 20 will be equal to even plus 20 minus one multiplied with D, which is equal to four plus 20 minus one multiplied with six, which is equal to 118 putting the value off a 20 a one in the summer of 20 terms will get some of 1st 20 terms is equal to 10 multiplied with four plus 118 which is equal to 10 multiplied with 122 which is equal to 1220

We have to find the some of the computer. First commentator off the arithmetic sequence that it's food, then 16 20 daughter door. So the general formulated any questions. So here it will be the common differences. Say this is six. So this will be six end and here it is, say, minus two. Plastic said our it in six and minus two. So this is the general formula off the arithmetic sequence and now we have to find a 20 year term. So it 20 will be six multiplied with 20 miners. So that will be 1 20 miners so that they won one it. And now we have toe find the S 20. So after days and divide with two in the 1st 10 plus that were dictum So this is any question 20. So this was 22 head with two and the first time a say four and the laughter makes one want it. And now here it will be 10 multiplied with so the city 118 plus two plus four. So this will be 1 22 and 10 multi pounded. 1 22 will give 12 to 0. So they say the S 20 off the

So we want to find the some of the 1st 120 terms and usually write it like this. That's the sum of the 1st 120 terms. And our sequence looks like this 14, 16, 18, 20. And we can see that it's arithmetic has a common difference up to And we can see that our first term is 14 and we can write a rule for the 10th colonel. We start with 14, we keep on adding on to and we would do that and -1 times. So there's a general rule or an explicit formula for finding our different terms. And we want to add up the first terms, there's the first term, second term. So on, I would like to know what the a sub 120th term is. So what is that? 120th term? And I know we're going to add up 120 terms, but what is that last term? Well, it's 14 plus two times 119. And when we find that we'll just quickly add that up. 14 plus two times 119 that comes out to be 252. So the very last term that we would have in our listing of 100 and 20 numbers is 252. And we want to find the sum of all those. And in general, I have my students memorize this in a singsong away. I say take first plus last Times end over two. So first plus last time sent over to first plus last time sent over to So to find 120th some we're going to take the first term plus the last term times the number of terms over to first plus last time sent over to. Yeah. And again sing song and I usually do what snaps? It's just kind of silly. But let me tell you people remember. And so we have 14 plus 252 and then it's going to be times 60. Okay. And this is a pretty darn fast way to add up 120 terms, but this only works if it's arithmetic, which it is arithmetic. So there is the sum of 120 terms. Pretty big.

We're being asked to find the some of the 1st 20 terms in the sequence. One plus five plus nine plus 13 etcetera. So to do this, we can use our summation formula s a Ben is equal toe end divided by two times the quantity of two times a someone plus and minus one times D because we know end and it's gonna be 20 because we're looking for the some of the 1st 20 terms. Ace of one is the first term, which is one, and we confined d are common difference are common difference. We simply just add for each time, So d is for so substitute these values into our formula. So we're gonna have s of 20 equals 20 divided by two times to quantity of two times one plus 20 minus one times four And now we just need to evaluate. Well, 20 divided by two is 10 two times one is two and 20 minus one is 19 and 19 times, for it is 76. So plus 76 well two plus 76 is 78 78 times 10 is 780. So the some of the 1st 20 terms for the Siri's would be seven


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