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sloppycanada

  • one year ago

I'm so confused on this, I'm not sure what I'm supposed to use for any of this, I don't know the common denominator or anything. Find the 6th term of the sequence with t1 = -4 and tn = 5tn-1. http://imgur.com/BaADfyq

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  1. ganeshie8
    • one year ago
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    start with \(-4\), and keep multiplying by \(5\) to get the next term.

  2. sloppycanada
    • one year ago
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    So T6 is -62,500?

  3. ganeshie8
    • one year ago
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    first term, \(\large t_1 ~=~-4\) second term, \(\large t_2 ~=~-4*5 = -20\) third term, \(\large t_3 ~=~-20*5 = -100\) keep going till the 6th term

  4. ganeshie8
    • one year ago
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    -62,500 is wrong

  5. sloppycanada
    • one year ago
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    Sorry, I did too many of them. -2500.

  6. ganeshie8
    • one year ago
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    show me the work instead

  7. sloppycanada
    • one year ago
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    T4 = -100 x 5 = -500 T5 = -500 x 5 = -2500 T6 = -2500 x 5 = -12500

  8. ganeshie8
    • one year ago
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    Good!

  9. sloppycanada
    • one year ago
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    And then how do I go about finding the sum of an infinite series?

  10. ganeshie8
    • one year ago
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    look at the terms : \[-4,~~-20,~~-100,~~-500,~~-2500,~~ \ldots\] what do you notice ? do they seem to converge to some number ?

  11. sloppycanada
    • one year ago
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    You could go on for ever without getting a sum.

  12. ganeshie8
    • one year ago
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    Yes, so we say the "sequence doesn't converge" and the infinite sum doesn't exist

  13. sloppycanada
    • one year ago
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    So for an equation like this - Find the sum of the infinite series 3 + 1.2 + 0.48 + 0.192 + ...if it exists. All I would do is use the formula to find the equation of the infinite series?

  14. ganeshie8
    • one year ago
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    what kind of series is it, geometric/arithmetic ?

  15. sloppycanada
    • one year ago
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    Geometric?

  16. ganeshie8
    • one year ago
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    there is a nice criterion for testing convergence of geometric series, you simply look at the common ratio

  17. ganeshie8
    • one year ago
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    whats the common ratio of given series ?

  18. sloppycanada
    • one year ago
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    The equation is tn/(tn-1)

  19. sloppycanada
    • one year ago
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    Common ratio is 2.5

  20. ganeshie8
    • one year ago
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    yes work it common ratio = (next term)/(present term)

  21. ganeshie8
    • one year ago
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    looks you have worked it in reverse : (present term)/(next term)

  22. ganeshie8
    • one year ago
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    try again

  23. sloppycanada
    • one year ago
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    .4?

  24. ganeshie8
    • one year ago
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    yes common ratio = 0.4 which is between -1 and 1 so the given series conveges

  25. ganeshie8
    • one year ago
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    A geometric series converges if the common ratio is between -1 and 1

  26. ganeshie8
    • one year ago
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    use infinite sum formula to find the sum

  27. ganeshie8
    • one year ago
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    do you have the formula wid u ?

  28. sloppycanada
    • one year ago
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    S(infinite) = 3/t-.4

  29. sloppycanada
    • one year ago
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    I have it in my notes

  30. ganeshie8
    • one year ago
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    \[\large S_{\infty} ~=~\dfrac{t_1}{1-r}\]

  31. ganeshie8
    • one year ago
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    \[\large S_{\infty} ~=~\dfrac{3}{1-0.4}\]

  32. ganeshie8
    • one year ago
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    simplify

  33. sloppycanada
    • one year ago
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    5?

  34. ganeshie8
    • one year ago
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    Yes!

  35. sloppycanada
    • one year ago
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    I have three more if you have time?

  36. ganeshie8
    • one year ago
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    okay il try, post

  37. sloppycanada
    • one year ago
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    http://gyazo.com/f47f214fcdb2adb56c90ca6794e3f48d

  38. ganeshie8
    • one year ago
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    Firs test if the series converges by finding the common ratio

  39. ganeshie8
    • one year ago
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    whats the common ratio ?

  40. sloppycanada
    • one year ago
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    1.33?

  41. ganeshie8
    • one year ago
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    Yes, which is "not" in between -1 and 1 so the series does not converge.

  42. ganeshie8
    • one year ago
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    we say the sum does not exist

  43. sloppycanada
    • one year ago
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    Okay so the answer would be "No solution"

  44. ganeshie8
    • one year ago
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    As you can see, the common ratio decides whether an infinite converges to some number, or if it diverges

  45. ganeshie8
    • one year ago
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    Answer would be "does not converge"

  46. sloppycanada
    • one year ago
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    If it converges then it has a sum, if it does not converge there is not really a solution?

  47. ganeshie8
    • one year ago
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    yes, do you see why the common ratio of 1.33 gives a diverging sum ?

  48. sloppycanada
    • one year ago
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    Because it's larger then 1? and not between that -1 and 1

  49. ganeshie8
    • one year ago
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    Yes, when you multiply the first term by 1.33, you get a bigger next term; the terms keep growing and the sum wont reach a specific number

  50. sloppycanada
    • one year ago
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    So for this problem - http://gyazo.com/15138c898cca305ec43a79e298d55821 The answer would be .498

  51. ganeshie8
    • one year ago
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    how did u get 0.498 ?

  52. ganeshie8
    • one year ago
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    im asking because im getting a more nice looking number : 0.5

  53. sloppycanada
    • one year ago
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    I didn't round.

  54. ganeshie8
    • one year ago
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    me neither could you show ur work please

  55. sloppycanada
    • one year ago
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    \[S \infty = \frac{ 1 }{ 3 }\div 1-.33\]

  56. ganeshie8
    • one year ago
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    Ahh okay, you're rounding 1/3 to 0.33

  57. ganeshie8
    • one year ago
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    i worked it like this : \[\large S_{\infty}~=~\dfrac{1/3}{1-1/3} = \dfrac{1}{3-1}=\dfrac{1}{2}=0.5\]

  58. sloppycanada
    • one year ago
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    I'm not sure why I changed from a fraction to a decimal. Fractions are more precise aren't they?

  59. ganeshie8
    • one year ago
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    Yep Fractions are exact decimals are not so exact when you get a repeating decimal

  60. ganeshie8
    • one year ago
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    1/2 = 0.5 both are exact

  61. ganeshie8
    • one year ago
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    1/3 = 0.33333333333333333333333333... clearly the decimal wont be exact because you can't write out infinitely many 3's

  62. sloppycanada
    • one year ago
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    Okay, last one - http://gyazo.com/50d340d91d94093d361677d900fa46ee Answer is 1.

  63. ganeshie8
    • one year ago
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    \[\huge \color{red}{\checkmark}\]

  64. sloppycanada
    • one year ago
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    Ah hah! Thank you!

  65. sloppycanada
    • one year ago
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    Not sure how to show my appreciation on this site (if there are points or something), but let me know if there is.

  66. ganeshie8
    • one year ago
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    yw! click the "Best Response" button next to any reply if you find the answer helpful

  67. ganeshie8
    • one year ago
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    you could also write a testimonial if you think the helper is amazing

  68. ganeshie8
    • one year ago
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    not encouraging you to write a testimonial for me right now, but just letting you know :)

  69. sloppycanada
    • one year ago
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    Finding the sum of an geometric Find S12 for the series 1 + 2 + 4 + 8 +... like this is 49,140

  70. ganeshie8
    • one year ago
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    go through this when u have time to know more about the site http://openstudy.com/code-of-conduct

  71. ganeshie8
    • one year ago
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    how did u get 49.140 ?

  72. sloppycanada
    • one year ago
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    Sorry it should be 8,190. 2((1-2^12)/(1-2)) = 8190

  73. sloppycanada
    • one year ago
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    |dw:1435126030016:dw|

  74. ganeshie8
    • one year ago
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    why are you multiplying by 2 ?

  75. ganeshie8
    • one year ago
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    first term is 1 right

  76. ganeshie8
    • one year ago
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    |dw:1435126092819:dw|

  77. sloppycanada
    • one year ago
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    Okay so it'd just be 4095

  78. ganeshie8
    • one year ago
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    Correct.

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