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. 1, 5, 9, 13,...

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 35th term of the sequence. So the sequence given to us is negative -8 -3 2. And continuing now in order to find the equation we need to use the general and the equation for any arithmetic sequence. And that's going to be a sub N. Is equal to the first term which is a sub one plus the quantity and minus one times the common difference which is D. Now we need to go ahead and figure out what a sub one and the common difference is a sub one represents the first term of any given arithmetic sequence. And here the first term is negative 13. So we're going to allow a sub one to equal to negative 13. Now we need to go ahead and find the common difference. Well for the common difference to go from negative 13 to negative eight we're going to add five to negative 13. To go from negative eight to negative three. We're going to add five to negative eight. And to go from negative three to positive two. We're going to add five to negative three. So as you can see for every term that we get in the arithmetic sequence we're going to add five to the current term. And that means that the current the difference is going to be positive five. So D. Is equal to five. Now we can go ahead and plug this into the equation for a sub N. To find the equation that describes the end term. So a sub N is going to equal to a sub one which is negative 13 plus the quantity and minus one times the common difference D. Which is five. And now I just need to go ahead and simplify in order to simplify, I'm going to distribute five into the quantity and minus one and that's going to give me negative 13 plus five N minus five. And now I just need to go ahead and combine like terms negative minus five is going to give me negative 18. So a sub N is equal to negative 18 plus five N. And that's going to be the equation that describes the end term of the arithmetic sequence. But this is only the first part of the answer because now we need to use this equation to find the 35th term of the arithmetic sequence. Since we want to find the 35th term, we're going to allow N two equal to 35 because N represents the amount of terms that are within your sequence. Since N is equal to 35 substituting this into the equation is going to give us a sub, 35 is equal to negative 18 plus five times 35 Five times 35 is going to give us 175 And negative 18 plus 175 is going to give me 157. So a sub 35 is equal to positive 157 and that's going to be the second half to the answer for this problem. So just to recap, the equation that describes, the 10th term is a sub N is equal to negative 18 plus five N. And the 35th term of the sequence is 157. With that being said, the answer to this problem is going to be C. 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. 1, 5, 9, 13,...