Correcting My Answer: Ensuring Accuracy and Improving Learning

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In summary, a student is asking for their answer to be checked and corrected if there are any mistakes. They are then given feedback on their mistake of using division instead of finding the ninth root, and also making an error in the substitution of variables. The conversation then continues with further discussion about finding the ninth root of -512 and a hint to try factoring.
  • #1
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Hi

I want check my answer and If there any mistake please correct it to me[/b]
 

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  • #3
what is the mistake ?
 
  • #4
-512 divided by 9 [itex]\approx[/itex] -56 (but not exactly)
But the ninth root is not division.

Anyway, following on from that mistake, when you used the formula:

[tex]\frac{a\left(1-r^n\right)}{1-r}[/tex]

You substituted incorrectly. a=1/4, r=-56 (your mistake), n=5 (since it asks for the 5th term)
This is what you had:
[tex]\frac{\frac{1}{4}\left(1-(-56)^9\right)}{1-(-9)}[/tex]

This is what you should have:
[tex]\frac{\frac{1}{4}\left(1-(-56)^5\right)}{1-(-56)}[/tex]

But anyway, following on from that mistake also, whatever happened to the [itex]1-r^n[/itex] part?

[itex]1-(-56)^9[/itex] all of a sudden became something like 5x4 from the looks of it, but since you end up with the answer of -5.7 from there, it means that part must've been equal to 182.4, but it doesn't seem like it is.

Honestly, you need to go back and revise your algebra. You will struggle to solve all these harder questions if you don't have a firm foundation with algebra.
 
  • #5
Oh and you wrote that the right-hand column is T10. The question says to find the 5th term (T5) and already gives you [itex]T_{10}=-128[/itex].
 
  • #6
You're given that a = -1/4 and T10 = -128, and you need to find the common ratio r.

T10 = ar9
==> -128 = (-1/4)r9
==> -512 = r9
==> [tex]r = \sqrt[9]{-512}[/tex]
As I said in my first post, the 9th root of -512 is not -56. If that were true (which it isn't), it would have to be the case that (-56)9 = -512.

By my calculator, (-56)9 = -5416169448144896, so that's off by quite a bit. So what is the correct ninth root of -512? Hint: try factoring -512.
 
  • #7
Thank D .mark
 

1. What is the importance of checking my answer?

Checking your answer is important because it ensures accuracy and understanding. By double-checking your work, you can catch any errors or misunderstandings and correct them before submitting your answer.

2. How can I check my answer effectively?

The most effective way to check your answer is to go through each step of your process and verify that it is correct. You can also ask a peer or mentor to review your answer and provide feedback.

3. What should I do if I find an error in my answer?

If you find an error in your answer, don't panic. Take a step back and retrace your steps to find where the error occurred. Once you have identified the mistake, correct it and double-check your work again.

4. Is it necessary to check my answer if I am confident in my work?

Yes, it is always necessary to check your answer, even if you are confident in your work. It is possible to overlook a mistake or misunderstanding, and checking your answer can help catch these errors before they become bigger issues.

5. How can I avoid making mistakes when checking my answer?

To avoid making mistakes when checking your answer, it is important to take your time and be thorough. It can also be helpful to use different methods or approaches to solving the problem to ensure that your answer is correct.

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