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=-20, d = -4

Accepted Answer

Hello. Today we are asked to find the equation that describes the end term of the following arithmetic sequence. And then we are asked to use that equation to find the 40th term of the sequence. So the general equation for the end term of any given arithmetic sequence is a sub N. Is equal to your first term. A sub one plus the quantity and minus one times D. Now in the problem we are we are told that the first term of the arithmetic sequence is a sub one is equal to 45 we are told that the common difference D. Is equal to negative nine. So we can go ahead and directly plug this into the general form of the 10th term in order to figure out what the equations of the NTT term is. And so making those substitution is going to give us a sub N. Which is equal to a sub one which is negative 45 plus the quantity and minus one times the common difference D. Which is negative nine. And now what we need to do is simplify. In order to simplify we're going to distribute negative nine into the quantity and minus one and that's going to give us negative 45 minus nine N plus nine. Because negative nine times negative one is going to give us positive nine and combining like terms together negative 45 plus nine is going to give us negative 36. So the equation that describes the general end term is going to be a sub N. Is equal to negative 36 minus nine N. And that's going to be the answer to the first part of this question. Now again we are asked to find the 40th term of this arithmetic sequence. Since we are asked to find the 40th term, we're going to allow end to equal to 40 because N represents the amount of terms there within your arithmetic sequence. And so plugging this into the general equation of the term is going to give us a sub Is equal to -36 -9 times 40. Now negative nine times 40 is going to give us negative 360. So we have negative 36 minus 360 negative 36 minus 360 is going to give us negative 396. So that means that the 40th term of this arithmetic sequence is equal to negative 396 and that's going to be the answer to the second part of this question. So again, the equation that describes the end term of the of the sequence is a sub N. Is equal to negative 36 minus nine N. And the 40th term is negative 396. With that being said, the answer to this problem is going to be a So I hope this video helps you in understanding how to find the equation of the end term of an arithmetic sequence and I'll go ahead and see you all in the next video.

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=-20, d = -4

Key Concepts

Arithmetic Sequence

General Term Formula

Finding Specific Terms

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