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anonymous

  • one year ago

Which of the following sequences of numbers are arithmetic sequences? Check all that apply. A. 54, 71, 88, 105, 122, ... B. 154, 71, 8, 5, 2, ... C. 345, 346, 347, 348, 349, ... D. 12, -24, 36, -48, 56, ... E. -3, -10, -17, -24, -31, ...

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  1. SolomonZelman
    • one year ago
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    a sequence that follows a pattern where you add the same number each time, or subtract the same number each time - is arithmetic sequence.

  2. anonymous
    • one year ago
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    ok

  3. anonymous
    • one year ago
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    its d/

  4. SolomonZelman
    • one year ago
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    For example: `1, 4, 7, 10, 13 ....` here you are adding 3 every time, and this is why it is an arithmetic sequience. ---------------------------------------------------- example #2: `6, - 10, -26, -52,....` here you are subtracting 16 every time, and this is why it is an arithmetic sequience.

  5. anonymous
    • one year ago
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    because it goes up by -7

  6. SolomonZelman
    • one year ago
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    you mean E?

  7. anonymous
    • one year ago
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    yea

  8. anonymous
    • one year ago
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    /lol

  9. SolomonZelman
    • one year ago
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    yes, and the common difference is -7 (you add -7, as you said - which is completely correct). Good job!

  10. anonymous
    • one year ago
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    thx

  11. SolomonZelman
    • one year ago
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    An alternating sequence is by definition not arithmetic, and thus must be excluded.

  12. SolomonZelman
    • one year ago
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    Hold on, there might be other options.....

  13. anonymous
    • one year ago
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    wait

  14. anonymous
    • one year ago
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    check all that apply

  15. anonymous
    • one year ago
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    theres more

  16. SolomonZelman
    • one year ago
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    Lets go in order. We know E is arithmetic (d=-7) We know D is NOT arithmetic (because the sign alternates) yes, thre is more...

  17. SolomonZelman
    • one year ago
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    can you name some?

  18. anonymous
    • one year ago
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    c

  19. SolomonZelman
    • one year ago
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    Yes, (d=1)

  20. anonymous
    • one year ago
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    so yes is right

  21. SolomonZelman
    • one year ago
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    there is a third correct answer (so far E and C are correct)

  22. anonymous
    • one year ago
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    8ummmmmm

  23. anonymous
    • one year ago
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    a

  24. SolomonZelman
    • one year ago
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    Yes, A (d=17)

  25. SolomonZelman
    • one year ago
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    So, A, C & E are sequences that are arithmetic:)

  26. anonymous
    • one year ago
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    thx

  27. SolomonZelman
    • one year ago
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    D is NOT arithmetic, because the sign alternates. ------------------------------------------- B is obviously NOT arithmetic, because there is no [same] common difference. 154 - 71 \(\ne\) 71 - 8 \(\ne\) 8 - 5

  28. SolomonZelman
    • one year ago
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    the difference is NOT ALWAYS the same, so for this reason B is NOT arithmetic....

  29. SolomonZelman
    • one year ago
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    Any questions about anything said in this post?

  30. anonymous
    • one year ago
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    nosir

  31. anonymous
    • one year ago
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    i got one more question

  32. SolomonZelman
    • one year ago
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    Sure:)

  33. anonymous
    • one year ago
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    A roll of paper towels is wound around a hollow cardboard tube. The cardboard tube in the middle of the roll has an outside radius of 2.4 cm. The thickness of the paper is 0.3 mm. The sequence of distances of the loops of paper away from the center of the roll (in centimeters) is the following: a1, a2, a3, a4, a5, & = 2.40, 2.43, 2.46, 2.49, 2.52, & What is the radius of the 85th loop of paper, starting from the center of the tube? A. 4.89 cm B. 4.92 cm C. 4.86 cm D. 4.95 cm

  34. SolomonZelman
    • one year ago
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    The distance of the loop of paper away from the center is the radius, right?

  35. anonymous
    • one year ago
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    yes

  36. SolomonZelman
    • one year ago
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    \(a_1\) is the very first radius

  37. SolomonZelman
    • one year ago
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    \(a_2\) is the second radius

  38. SolomonZelman
    • one year ago
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    and you need \(a_{85}\) - the 85th radius.

  39. anonymous
    • one year ago
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    yep

  40. SolomonZelman
    • one year ago
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    So, lets take a look at the given information.

  41. SolomonZelman
    • one year ago
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    \(\color{black}{a_1=2.40}\) \(\color{black}{a_2=2.43}\) \(\color{black}{a_3=2.46}\) \(\color{black}{a_4=2.49}\) \(\color{black}{a_5=2.52}\)

  42. SolomonZelman
    • one year ago
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    What is the common difference here?

  43. anonymous
    • one year ago
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    0.03

  44. SolomonZelman
    • one year ago
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    Yes, that is correct!

  45. SolomonZelman
    • one year ago
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    I assume you have seen the following formula previously: \(\color{black}{\large a_n=a_1+{\rm d}\cdot (n-1)}\)

  46. SolomonZelman
    • one year ago
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    1) you have to find the 85th term, so you would plug in n=85. 2) you know the first term is 2.40 (so you plug in \(a_1=2.40\) 3) you know the common difference is 0.03 (so plug in d=0.03).

  47. SolomonZelman
    • one year ago
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    \(\color{black}{\large a_{85}=2.40+{\rm 0.03}\cdot (85-1)}\) \(\color{black}{\large a_{85}=?}\)

  48. anonymous
    • one year ago
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    4.92

  49. SolomonZelman
    • one year ago
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    yes, that is right. And that means that your 85th radius is 4.92 centimeters.

  50. anonymous
    • one year ago
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    thx

  51. SolomonZelman
    • one year ago
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    yw

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