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JozelynW

  • one year ago

I need help............ I don't know how to convert f(n)=f(n-1)+d into the sequence notation a(subscript) n=a+d(n-1)

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  1. JozelynW
    • one year ago
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    @dan815

  2. jim_thompson5910
    • one year ago
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    is that all it says? or is there more that's given?

  3. JozelynW
    • one year ago
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    No it says "Use your scenario to write the function for the 7th term in your sequence using sequence notation".

  4. JozelynW
    • one year ago
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    this is what i filled in Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for 20 minutes on Monday. Every day she increases her practice time by 4 . If she continues this pattern, how many minutes will she practice on the 7th day? Be sure to fill in the blanks with the words that will create an arithmetic sequence. Use your scenario to write the function for the 7th term in your sequence using sequence notation.

  5. JozelynW
    • one year ago
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    20 mins , increases , time by 4 that's what i added

  6. jim_thompson5910
    • one year ago
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    so they want you to make up a sequence of your own? or can we use this example?

  7. JozelynW
    • one year ago
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    they wanted me to make up my own based upon what i filled in and the formula above with the a

  8. jim_thompson5910
    • one year ago
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    ok what sequence did you make up on your own?

  9. JozelynW
    • one year ago
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    a(subscript) n=a+d(n-1)

  10. JozelynW
    • one year ago
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    that is what help on filling in on this equation. In the f(n) version it made up one which is f(7)=f(6-1)+4

  11. JozelynW
    • one year ago
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    when i fill in the sequence equation it looks like this a(subscript)7=a+4(7-1)

  12. jim_thompson5910
    • one year ago
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    it says `Jasmine practices the piano for 20 minutes on Monday` so the first term of this sequence is 20 making a = 20

  13. jim_thompson5910
    • one year ago
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    the next day, tuesday, would be a+d = 20+4 = 24 min ------------------------- wednesday would be 24+4 = 28 etc etc

  14. JozelynW
    • one year ago
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    so how would that be written

  15. jim_thompson5910
    • one year ago
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    a = 20 and d = 4 they are plugged into `a+d(n-1)` to get the general nth term

  16. jim_thompson5910
    • one year ago
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    so, a+d(n-1) = 20+4(n-1) = ???

  17. JozelynW
    • one year ago
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    thank you for you help.

  18. jim_thompson5910
    • one year ago
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    glad to be of help

  19. JozelynW
    • one year ago
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    @jim_thompson5910 need you help again with another 1

  20. jim_thompson5910
    • one year ago
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    go ahead

  21. JozelynW
    • one year ago
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    Use your scenario to write the formula for the 5th term in your sequence using sequence notation.

  22. JozelynW
    • one year ago
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    the equation for geometric sequence is an=a1•rn−1.

  23. JozelynW
    • one year ago
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    my info is Anthony goes to the gym for 45 minutes on Monday. Every day he increases his gym time by 5 minutes.

  24. jim_thompson5910
    • one year ago
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    `Anthony goes to the gym for 45 minutes on Monday. Every day he increases his gym time by 5 minutes.` this is an ARITHMETIC sequence since the amount is increasing by a fixed amount. d = 5 is the amount going up each time

  25. jim_thompson5910
    • one year ago
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    if you said maybe something like "increases by 5%", then it would work

  26. JozelynW
    • one year ago
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    i see what you're saying , I knew something wasn't right. So change it to 5%

  27. JozelynW
    • one year ago
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    then what would i do

  28. jim_thompson5910
    • one year ago
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    the first term is a = 45 the common ratio is r = 0.05 (decimal form of 5%)

  29. jim_thompson5910
    • one year ago
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    no sorry, the common ratio would be 1.05 1+0.05 = 1.05

  30. JozelynW
    • one year ago
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    so it would be a5=45 x1.05(7-1)

  31. jim_thompson5910
    • one year ago
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    first term: 45 second term = (first term)*(common ratio) second term = (45)*(1.05) second term = 47.25 etc etc

  32. JozelynW
    • one year ago
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    change the 5% to 1.05%?

  33. jim_thompson5910
    • one year ago
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    I added on 1 because increasing by 5% is the same as multiplying by 1.05

  34. jim_thompson5910
    • one year ago
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    the nth term should be \[\Large a(r)^{n-1}\] then you plug in a = 45 and r = 1.05

  35. JozelynW
    • one year ago
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    ok

  36. JozelynW
    • one year ago
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    i have to use that exact equation above \[a _{4=45x 1.05(4}\]

  37. JozelynW
    • one year ago
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    the x= times

  38. jim_thompson5910
    • one year ago
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    the exponent should be n-1 = 4-1 so \[\LARGE a_4 = 45*(1.05)^{4-1}\]

  39. JozelynW
    • one year ago
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    well no, because i want to find the 5th term. I simplified it so I didn't put the -1 i just did it.

  40. JozelynW
    • one year ago
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    so 5-1

  41. jim_thompson5910
    • one year ago
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    oh, then you want to compute \(\LARGE a_5\) and not \(\LARGE a_4\)

  42. JozelynW
    • one year ago
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    yes it's a5 not a4

  43. JozelynW
    • one year ago
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    they wanted me to find a5 the fifth term.

  44. jim_thompson5910
    • one year ago
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    I see

  45. JozelynW
    • one year ago
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    ok so the answer would be what i said rightttt

  46. jim_thompson5910
    • one year ago
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    yes, it would be \[\LARGE a_5 = 45*(1.05)^{4}\]

  47. JozelynW
    • one year ago
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    Thank you, I may need help in like 3 mins again 1 more

  48. jim_thompson5910
    • one year ago
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    ok

  49. JozelynW
    • one year ago
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    a_(5=45 ×〖1.05〗^(5-1) ) @jim_thompson5910

  50. JozelynW
    • one year ago
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    Use your scenario from part 2 to write a question that will lead to using the geometric series formula. Use the formula to solve for Sn in your scenario.

  51. jim_thompson5910
    • one year ago
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    I think you meant to write \[\LARGE a_5 = 45 \times 1.05^{5-1}\] right?

  52. JozelynW
    • one year ago
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    Yes, but i don't know how to make it look like that, how do you do that?

  53. JozelynW
    • one year ago
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    the geometric series formula Sn= a1−a1rn 1−r

  54. jim_thompson5910
    • one year ago
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    you can use the equation editor (click the equation button below the text box) I typed in `\LARGE a_5 = 45 \times 1.05^{5-1}` surrounded by `\[` and `\]`

  55. jim_thompson5910
    • one year ago
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    as for the summation formula, it would be \[\Large S_n = a*\frac{1-r^n}{1-r}\]

  56. jim_thompson5910
    • one year ago
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    which is equivalent to the form you wrote

  57. JozelynW
    • one year ago
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    where the a is by itself it should be with the 1 at the top

  58. jim_thompson5910
    • one year ago
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    yes the two are equivalent \[\Large S_n = a*\frac{1-r^n}{1-r} = \frac{a-a*r^n}{1-r}\]

  59. JozelynW
    • one year ago
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    I'm going to screenshot it

  60. JozelynW
    • one year ago
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  61. jim_thompson5910
    • one year ago
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    yeah which is what I wrote here \[\Large S_n = \frac{a-a*r^n}{1-r}\]

  62. jim_thompson5910
    • one year ago
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    there are 2 versions of the same thing really

  63. JozelynW
    • one year ago
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    ok

  64. JozelynW
    • one year ago
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  65. jim_thompson5910
    • one year ago
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    they want you to add up a bunch of terms and use the Sn formula to do it quickly

  66. jim_thompson5910
    • one year ago
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    so for instance, add up the first 8 terms and compute S8

  67. JozelynW
    • one year ago
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    So I"m using what you are saying as a example, because Idon't want to seem as a cheater

  68. jim_thompson5910
    • one year ago
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    you can use another value of n

  69. JozelynW
    • one year ago
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    ok 5

  70. JozelynW
    • one year ago
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    Oh it says use the same scenario

  71. JozelynW
    • one year ago
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    from part 2

  72. jim_thompson5910
    • one year ago
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    so a = 45 and r = 1.05

  73. JozelynW
    • one year ago
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    right ,but i need to make a question now

  74. JozelynW
    • one year ago
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    Maybe I can say Anthony goes to the gym at 10 am for 45mins, then IDK what im doing

  75. jim_thompson5910
    • one year ago
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    so you have to make a completely different scenario?

  76. JozelynW
    • one year ago
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    no just use the scenario from part 2 to make up a question

  77. JozelynW
    • one year ago
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    i just seen an example on my math lesson so here is something similar "find the sum of the first 5 terms of the geometric series

  78. JozelynW
    • one year ago
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    but I don't know what numbers are suppose to be in the geometric series here is the example

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  79. jim_thompson5910
    • one year ago
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    ok so you'll plug a = 45 and r = 1.05 into that Sn formula then you pick any n value you want (you picked n = 5 I think) and plug that in as well

  80. jim_thompson5910
    • one year ago
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    \[\Large S_n = \frac{a-a*r^n}{1-r}\] \[\Large S_5 = \frac{45-45*1.05^5}{1-1.05}\] \[\Large S_5 = ???\]

  81. JozelynW
    • one year ago
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    is it like the example?

  82. jim_thompson5910
    • one year ago
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    yes

  83. JozelynW
    • one year ago
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    ok than so what would be the geometric series than for the question?

  84. jim_thompson5910
    • one year ago
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    I'm not sure what you're asking exactly?

  85. JozelynW
    • one year ago
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    because i need to write a question; in the example question in the lesson it has something in the question that says geometric series look at the screenshot again

  86. JozelynW
    • one year ago
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    I think it means 3 numbers that have a common ratio of 5%

  87. jim_thompson5910
    • one year ago
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    you mean they want you to add up the first three terms of the geometric sequence?

  88. JozelynW
    • one year ago
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    idk honestly. I'm just listening to you

  89. JozelynW
    • one year ago
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    does it look like what it mean in the picture

  90. JozelynW
    • one year ago
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    this is a project and it doesn't really explain much

  91. jim_thompson5910
    • one year ago
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    yeah I wish it had clearer instructions. I think they want you to add up a bunch of terms so say you wanted to add up the first 7 terms a = 45 r = 1.05 n = 7 \[\Large S_n = \frac{a-a*r^n}{1-r}\] \[\Large S_7 = \frac{45-45*1.05^7}{1-1.05}\] \[\Large S_7 = \frac{45-45*1.4071004}{1-1.05}\] \[\Large S_7 = \frac{45-63.319518}{1-1.05}\] \[\Large S_7 = \frac{-18.319518}{-0.05}\] \[\Large S_7 = 366.39036\] The approximate sum of the first 7 terms is 366.39036

  92. JozelynW
    • one year ago
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    So the question would be "Find the sum of the first 7 terms

  93. jim_thompson5910
    • one year ago
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    yes the work shown above would apply to that question

  94. JozelynW
    • one year ago
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    Thank you, your name should say lifesaver. You just helped me finish out my math class.

  95. jim_thompson5910
    • one year ago
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    I'm glad I could be of help

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