In Exercises 23–34, write a formula for the general term (the nth...

Question

In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1 = 9, d=2

Accepted Answer

Hello. Today we're going to find the equation that describes the end term of the following arithmetic sequence. Then we're going to use that equation to find the 30th term of the arithmetic sequence. So the general form of the term of any arithmetic sequence is given as a sub N is equal to your first term, a sub one plus the quantity and minus one times the common difference which is D. Now in the problem here we are told that the first term of the arithmetic sequence is a sub one is equal to 22 we are told that the common difference D is equal to six. So what we're going to do is plug in these values into a sub N. That way we can find the equation that describes the end term of the arithmetic sequence. So doing so is going to give us a sub N is equal to a sub one which is 22 plus the quantity and minus one times D which is six. And now we just need to go ahead and simplify. In order to simplify, I'm going to distribute six into the quantity and -1 and that's going to give me a sub N is equal to 22 plus six and minus six. And now I'm going to go ahead and combine like terms minus six is going to give me 16. So I have a sub N is equal to 16 plus six N. And this is going to be the equation that describes the end term of our arithmetic sequence. Now this is only the first answer because now we need to use this equation to find the 30th term of the sequence. Since we are asked to find the 30th term of the sequence, we're going to allow N two equal to 30 because N represents the amount of terms that are within your sequence. So plugging an end for 30 into the equation is going to give us a sup 30 is equal to 16 plus six times 30. Now six times 30 is going to give us And 16 plus 180 is going to give us 196. So the 30th term a sub 30 is equal to 196 and that's going to be the other answer to this problem. So the equation that describes the end term is going to be a sub N is equal to 16 plus six N. And the 30th term is 196. With that being said, the answer to this problem is going to be be so I hope this video helps you in understanding how to find the anti equation for an arithmetic sequence and I'll go ahead and see you all in the next video

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In Exercises 23–34, write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for to find the 20th term of the sequence. a1 = 9, d=2