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LilyMQ

  • one year ago

What is the sum of a 23-term arithmetic sequence where the first term is 9 and the last term is 119?

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  1. LilyMQ
    • one year ago
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    Is it 1472? That's what I got

  2. Jhannybean
    • one year ago
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    First define what an arithmetic sum is.

  3. SolomonZelman
    • one year ago
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    i think you are a little off

  4. LilyMQ
    • one year ago
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    So it's wrong?

  5. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle a_9=9 }\) \(\large\color{black}{ \displaystyle a_{23}=119 }\) \(\large\color{black}{ \displaystyle {\rm S}_{23-9}=\frac{\left(a_9+a_{23}\right)}{2} \times(23-9) }\) \(\large\color{black}{ \displaystyle {\rm S}_{23-9}=\frac{\left(9+199\right)}{2} \times(23-9) }\)

  6. SolomonZelman
    • one year ago
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    where 23-9 is the number of terms, and the first fraction is the average term

  7. LilyMQ
    • one year ago
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    is it 1456?

  8. Jhannybean
    • one year ago
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    That is, \[\large S_n=\frac{n(a_1+a_n)}{2}\]To find \(a_n\) we need to use an arithmetic sequence, \(a_n = a_1 +(n-1)d\)

  9. LilyMQ
    • one year ago
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    okay

  10. SolomonZelman
    • one year ago
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    we know the 23rd term, Jhanny....

  11. Jhannybean
    • one year ago
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    Yeah I just reread it haha

  12. SolomonZelman
    • one year ago
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    i think all you need is last+first term \(a_{23}\) and \(a_9\) in this case....

  13. SolomonZelman
    • one year ago
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    alright....

  14. SolomonZelman
    • one year ago
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    1456 is right....

  15. SolomonZelman
    • one year ago
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    1456 apples, jk

  16. Jhannybean
    • one year ago
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    but whats with the multiplication?

  17. LilyMQ
    • one year ago
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    then what?

  18. SolomonZelman
    • one year ago
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    multiplication ?

  19. SolomonZelman
    • one year ago
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    (9+199)÷2 => the average term 23-9 = number of terms (9+199)÷2 • (23-9) = the sum of all terms together

  20. Jhannybean
    • one year ago
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    \[\large S_{23} = \frac{23(9+119)}{2}\]

  21. SolomonZelman
    • one year ago
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    not 23

  22. SolomonZelman
    • one year ago
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    you don't add the terms before \(a_9|)

  23. SolomonZelman
    • one year ago
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    oh, my bad

  24. LilyMQ
    • one year ago
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    so it is 1472?

  25. SolomonZelman
    • one year ago
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    what the hell am I saying....Jhanny, i am a laborer before thee

  26. Jhannybean
    • one year ago
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    You wrote 199 instead of 119 O_o

  27. SolomonZelman
    • one year ago
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    i read \(a_9\) with my blind eyes.

  28. Jhannybean
    • one year ago
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    and @LilyMQ I have no idea. No calculator here, just helping you understand the format :)

  29. SolomonZelman
    • one year ago
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    9 is the 1st term... then it is completely off....

  30. SolomonZelman
    • one year ago
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    (9+199)÷2 => the average term 23 = number of terms (9+199)÷2 • 23 = the sum of all terms together

  31. SolomonZelman
    • one year ago
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    sorry for my mistake.

  32. LilyMQ
    • one year ago
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    oh, so it's 2392?

  33. SolomonZelman
    • one year ago
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    yes, this is correct

  34. SolomonZelman
    • one year ago
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    and this time, it is correct for real:D

  35. LilyMQ
    • one year ago
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    Yay. Okay thanks guys!

  36. LilyMQ
    • one year ago
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    Wait wait

  37. LilyMQ
    • one year ago
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    That doesn't make sense. These are the options 1,219 1,472 1,725 1,978

  38. LilyMQ
    • one year ago
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    HELPP

  39. SolomonZelman
    • one year ago
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    the first term is 9 the last (i.e. 23rd) term is 199 are you sure about this information ?

  40. LilyMQ
    • one year ago
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    What is the sum of a 23-term arithmetic sequence where the first term is 9 and the last term is 119?

  41. LilyMQ
    • one year ago
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    119 not 199 lol

  42. SolomonZelman
    • one year ago
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    oops my fault again, i will try to, if i can, to refrain from my mistake

  43. SolomonZelman
    • one year ago
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    i will re-correct my post again. tnx for catching the err.

  44. LilyMQ
    • one year ago
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    haha it's okay

  45. SolomonZelman
    • one year ago
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    (9+119)÷2 => the average term 23 = number of terms (9+119)÷2 • 23 = the sum of all terms together

  46. SolomonZelman
    • one year ago
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    u were correct initially....

  47. LilyMQ
    • one year ago
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    o

  48. LilyMQ
    • one year ago
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    okay thank you lol

  49. SolomonZelman
    • one year ago
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    You are like :O and I am like Oh..... my fault, lol

  50. SolomonZelman
    • one year ago
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    thank YOU for catching it.... with me you would have gone into the forest of unnecessary wonders.

  51. SolomonZelman
    • one year ago
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    Good luck:)

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