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The 4th term of a geometric sequence is 18, and the 10th term is 162. What is the 7th term?

 May 3, 2022
 #1
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I hope this is correct.

162/18 = 9. Since 6 terms later from the 4th term is 18, we have to multiply by sqrt(3) each time. 18*3sqrt(3) = 54sqrt(3).

 May 3, 2022
 #2
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so, I saw the equation on this same problem in here, so  if the 4th term is 18 and the 10th term is 162:

 

18 * d^6 = 162

d= 91/6

 

18 * d3 = a7

18 * (91/6)3  = 18 * 3 = 54

 May 3, 2022
 #4
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You missed that d could also be negative. Also your value of d is not correct.

MaxWong  May 3, 2022
 #5
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you're saying that about their way of solving it but, bruh they said they saw it in here somewhere so technically it's not theirs, so they're not incorrect, whoever gave that to them is inncorrect. Next time for future, just post your way of solving it and let the person who asked the question choose because here's a good question for anybody and everybody on here, what if you are wrong too??? just saying.....

Guest May 3, 2022
 #6
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If they are copying from somewhere, they have the responsibility to check if the solution is correct. I am just telling the person that this solution is wrong, because it is good for the discussion. 

 

If you think I'm the one who is wrong, you can tell me. We can discuss. After all, this site is a forum.

MaxWong  May 3, 2022
 #7
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it's not called copying really, especially if they got the help, And slow down, i never said you were wrong, but just so you wont upset anyone on here just write your way of doing it. because you just never know, you may be wrong sometimes, and you just dont want to just say someone is wrong, they may very well be wrong, but you also need to be careful because no one really knows anyone here and someone can take that very hard or get offended. And i'm just speaking out as an adult and perspective. instead of saying what u said you could have said, "are you sure your d is correct maybe you should double check" or something. 

Guest May 4, 2022
 #8
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Um, okay,  i'll check that out then i still got the same answer, and fyi i didn't copy sooooo....yeafrown

Guest May 4, 2022
 #9
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I did a Repost so there wouldn't be any confuion: Um, okay,  i'll check that out then i still got the same answer, and fyi i didn't copy sooooo....yeafrown 

 

Also I saw that latest post in here overall and whoever wrote that "WHAT?!" thread is right, it can come across as mean sometimes, but i didn't take it the wrong way just fyi but still someone else could have.

Guest May 4, 2022
 #3
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The nth term of a geometric sequence is \(ar^{n - 1}\), where a is the first term and r is the common ratio.

 

We can find a and r with the given information. 

\(\begin{cases}ar^3 = 18\\ar^9 = 162\end{cases}\)

 

Then 

\(r ^6 = 9\\ r = \pm \sqrt[3]{3}\)

 

The 7th term is \(18 \cdot r^3 = \pm54\), where the sign depends on the sign of r.

 May 3, 2022

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