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LilyMQ

  • one year ago

Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95.

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  1. LilyMQ
    • one year ago
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    a. 203 b. 197 c. 168 d. 163

  2. Jhannybean
    • one year ago
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    Define what an arithmetic sequence is first. Do you know general form?

  3. LilyMQ
    • one year ago
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    I have no idea what any of this is lol

  4. Jhannybean
    • one year ago
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    Alright, so an arithmetic sequence is defined by the general form: \[\large a_n = a_1 + (n-1)d\]

  5. LilyMQ
    • one year ago
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    okay

  6. LilyMQ
    • one year ago
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    how can I calculate the common difference?

  7. Jhannybean
    • one year ago
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    @aric200 no need to criticize.

  8. Jhannybean
    • one year ago
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    n = the number of terms you're looking for in the sequence d = difference between the terms (preceding number - previous number) \(a_1\) = the first value in the sequence of numbers.

  9. LilyMQ
    • one year ago
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    oooh okay thank you

  10. Jhannybean
    • one year ago
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    So if we have \(a_{\color{red}n} = a_{\color{red}{18}}\) what does that tell you about the number of terms in the sequence?

  11. aric200
    • one year ago
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    I'm simply trying to say your teacher more than likely gave you background on what you are doing in less this is a pretest in which you should not even be asking for our help, but If not then I'm sure there is text that pertains to this type of math and going back over that could help you get a better understanding. Thats the best thing to do when you "have any idea what this is"

  12. aric200
    • one year ago
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    That is all but continue with your explanation.

  13. LilyMQ
    • one year ago
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    @Jhannybean does that mean you are trying to find the 18th term?

  14. LilyMQ
    • one year ago
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    how do I find 'd'?

  15. aric200
    • one year ago
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    She gave you the formula an = a1 + (n – 1)d

  16. LilyMQ
    • one year ago
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    I got a(31)=38+(31-1) but I'm not sure how to find d

  17. Jhannybean
    • one year ago
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    We are given \(\large a_{18} = a_n = 95\) That means if we take a closer look at this relation, we see that \(n=18\)

  18. Jhannybean
    • one year ago
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    This is basically telling us that if we had a 18 numbers in a sequence, our value of \(a_n\) would be 95.

  19. LilyMQ
    • one year ago
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    ooh ok

  20. Jhannybean
    • one year ago
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    So far we have :\[95 =-7+(18 - 1)d\] Are you following?

  21. LilyMQ
    • one year ago
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    yea

  22. Jhannybean
    • one year ago
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    Now can you solve d for me?

  23. LilyMQ
    • one year ago
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    is d 6?

  24. Jhannybean
    • one year ago
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    Yes, so \(d=6\). Now we're trying to find the 35th term in the sequence, this means we are trying to find \(a_n\) when \(n=35\)

  25. Jhannybean
    • one year ago
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    Now that we've found \(d=6\), it should be easy :)

  26. LilyMQ
    • one year ago
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    I got 197 for the answer. Is this correct?

  27. Jhannybean
    • one year ago
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    That is correct :D

  28. LilyMQ
    • one year ago
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    YAY! Thank you so much!

  29. aric200
    • one year ago
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    Here it is all together for you and anyone else who stumbles upon this question later. Makes it less complicated in my opinion but good job. x(n)=a+d(n-1) 95=-7+d(18-1) 95=-7+d(17) 95+7=d(17) 102=17d d=102/17 d=6 After finding D plug it in x(35)=-7+6(35-1) x(35)=-7+6(34) x(35)=-7+204 x(35)=197 So the answer is B) 197

  30. LilyMQ
    • one year ago
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    Awesome, thanks guys

  31. Jhannybean
    • one year ago
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    \[a_n= -7 +(35-1)(6)\]\[a_n=-7+204\]\[a_n = 197~ \checkmark \]

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