5

The eighth term in an arithmetic sequence is $5,$ and the sum of the first 10 terms is $20 .$ Find the common difference and the first term of the sequence....

Question

The eighth term in an arithmetic sequence is $5,$ and the sum of the first 10 terms is $20 .$ Find the common difference and the first term of the sequence.

The eighth term in an arithmetic sequence is $5,$ and the sum of the first 10 terms is $20 .$ Find the common difference and the first term of the sequence.



Answers

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

About our 100 current, which is a 100 is equal to negative 7 50 And then our common difference B is equal to negative 20 and were asked to find our 50 years. That's 85. Okay, so let's write out our formula for a 100. So we know that a 100 is equal to negative out of 7 50 which is equal to our first term, a one plus de which is negative. 20 plunge and minus one. And in this case, our end is 100. So we have 100. Let's one negative 20 times my engine. Right. This one is equal to negative 198 girl. And that will add 1982 websites to solve for 81 and then be right, um, our formula for our terms. Okay, so we get that anyone is equal to 1230 So our equation for our general form is a physical to our first term, plus our common difference Climes and minus one. Okay, I know it's all for our 15 so that's a fine. You go to 1230 minus 20 times five minutes. One plugging that into my God. I get that a five is equal to 115

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

And discussion we are given with the cities one plus five plus nine plus 13 plus upto 20 times. So we have Evan equals to one and B was 25 minus one, which is 1/4 full so we can give a 20 equals two even plus a 19 d, which is equal to one plus 19 multiplied with four which is equals to 77. Therefore, we can view some up to 20 terms as 20 divided by two multiplied with even that is full one close a 20 that is 77. That means we have the formula as s n is closed toe end divided by two multiplied with even plus a And therefore we have s 20 was too 780 that is evidence

1st 5 terms of the sequence to find as the first term being eight. The common difference of being negative five. Every fund, his 1st 5 terms. It wants us to find the 25th. Okay, So for the 1st 5 terms, we know that our first term is eight. Our second term. We're going down by five. Each time. It's gonna be three Negative. Too negative. Seven Negative. 12. There's our 1st 5 terms, Divine. Our 25th term was gonna use our formula. So we took our first term eight. We're gonna add in minus one. So in this case will be 24 and then our common differences negative times are coming. Difference. Which is negative. Five. 24 times negative. Five is negative. 120 eight plus negative. 1 20 So our 25th term is just gonna be negative. 112. Thank you very much.


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