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Find the common difference of an arthmetic sequence whose first term is 9 and whose eighth term isThe common difference is d =...

Question

Find the common difference of an arthmetic sequence whose first term is 9 and whose eighth term isThe common difference is d =

Find the common difference of an arthmetic sequence whose first term is 9 and whose eighth term is The common difference is d =



Answers

Find the $n$ th term of the arithmetic sequence with given first term $a$ and common difference $d .$ What is the 10 th term? $$ a=9, \quad d=4 $$

We need to find the 16th term off an arithmetic sequence whose first term, a one is equal to nine and the common differences to now we know that the in its term often arithmetic sequence is equal toe a one plus and minus one multiplied with D. Now, therefore, a 16 will be equal to nine plus 16 minus one multiplied with two, which is equal to nine plus 30 which is equal to 39.

We want to find the fourth term of the arithmetic sequence, whose first term is nine and whose common differences five. You will recall that the term of a Eric Medic sequence is equal to the first term, plus the common difference times on minus one. So since we're looking for the fourth term and is equal to four, that's going to be a four is equal to a one, which is nine plus the common difference. That's five times one minus one, which is, well, this works out to be 24.

We are going to do problem number 37. And this question, what we need to do is we need to find the first time. Common difference of the automatics automatic sequence described. Okay, So we have been given 14th town, There is -1. We have been given 18th term, that is a Menace name. And it is us to write when the curse the formula. So because the formula we will use there is a next time equals two Air plus and Venezuela including. Okay, now as it is 14 terms, so we can write this, it will be equals two A plus and minus one. That is 14 minutes one. So this is 13 lee. Now, similarly this is 18th term. So you're right, this is a plus 18 minutes one, that is 17 d. Next we are going to just sub strapped this two equations so minus minus nine plus nine plus nine minus one. So this will become Plus 9 -1. This will become eight equals two. They will get cancelled out now -17 Plus 13 -17 and plus 13. So this will be calls to menace for the from her day is coming out to be managed to common differences managed to no. What we'll do next is we are going to put the value of the and the equation one that is a plus 13 d Equals 2 -1 to find the value of a. So uh Plus 13 into managed to so the Silicon managed during the 60 calls to Venezuela. So from here adding 26 both sides. So this will be close to ah 25. Okay, 25 calls 2 25. Now we have a we have the we can write and some equation that is written as A plus and -1 injury. Okay So a here is 25. The hair is managed to so and when I went in to manage to let us solve this equation, 25 plus now managed to into end. So the slogan managed to end, Now managed to into management of the Silicon Plus two. So we are getting 27 managed to and So we got to be an entrance equation that is 27 minutes. Doing so. This is the answer in this case, That's all. Thank you.

In this problem. We're told that we're going to find the eighth term of the sequence that has a first term of nine. The common difference of six. Well, because our first term is nine, you'll see that I listed that a sub one is equal tonight and we're told the common differences six. So I looked That d is equal to six on. We're being asked to find the eighth term in the sequence. Well, because we're being asked to find the eighth term that represents our in value. So we know the end is equal to eight. So now we're going to use our formula that's used to find the EMP terminal sequence, which is a seven is equal to a sub one, plus the quantity and minus one times D, and we're going to substitute the values that we know into this equation. So we're finding a city because we're looking for the eighth term equals ace of one, which is nine plus the quantity of n, which is a minus one times D, which is six. And now we just have to simplify this Well, we're gonna have a C B is equal to well eight minus one is seven and seven times six is 42. So we have nine plus 42 9 plus 42 is 51 so the eighth term in the sequence would be 51.


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