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anonymous

  • 5 years ago

I need help with a sequence

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  1. anonymous
    • 5 years ago
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    10 13 16 8 If i is multiple of 4 divide it by 2 if it is not a multiple of 4 add 3 Find the 500th term The 500th term is 8 but i need a formula to show how i worked it out

  2. watchmath
    • 5 years ago
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    10,13,16,8,11,14,17,20,10,13,16,8 Then we can see that \(a_4=a_{12}=8\) and in general \(8=a_4=a_{4+8n}\) for any \(n\). Since \(500=4+8n\Leftrightarrow 496=8n\Leftrightarrow n=124 \) then \(a_{500}=8\).

  3. anonymous
    • 5 years ago
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    1. 8+3=11 2. 11+3=14 3. 14+3=17 4. 17+3=20 5. 20/2=10 6. 13 7. 16 8. 8 this will be repeating now the 4th element is 8 plus every 4+k8 element (k is an integer) 500=4+62*8 so it is 8

  4. watchmath
    • 5 years ago
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    Andras is right for the \(n\) :).

  5. anonymous
    • 5 years ago
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    The rule is if it is a multiple of 4 divide it by 2 so 8/2 =4/2=2+3=5+3=8/2=4/2=2+3=5

  6. anonymous
    • 5 years ago
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    that is what keeps on happening

  7. anonymous
    • 5 years ago
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    haha watchmath we both suck :)

  8. anonymous
    • 5 years ago
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    10 13 16 8 below four will be repeating than 4 2 5 8 so we can see that every 4th element is 8. 500/4=125 this proves that it is 8

  9. anonymous
    • 5 years ago
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    but 500 also divides by 4 so how can u be certain that it is 8

  10. anonymous
    • 5 years ago
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    every 4th element is an 8 (we can see that now) so if an element can be written as the the factor of 4 than it is 8. 1*4th element=8 2*4th =8 3*4th =8 and so on so the 125*4th element (500)=8

  11. anonymous
    • 5 years ago
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    ok thank you very much for helping me

  12. anonymous
    • 5 years ago
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    no prob

  13. anonymous
    • 5 years ago
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    What is the formula

  14. anonymous
    • 5 years ago
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    I dont think there is a formula here, you have to use your brain

  15. anonymous
    • 5 years ago
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    Are you sure because my dad says there is a formula but will not tell me

  16. anonymous
    • 5 years ago
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    the formula us that if the number can be written as 4k (k is an integer) than it is 8, I dont see what your dad wants.

  17. anonymous
    • 5 years ago
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    ok thanks i will go now and prove my dad wrong

  18. anonymous
    • 5 years ago
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    Good luck for that! :-)

  19. watchmath
    • 5 years ago
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    Well you can make a formula \(a_1=10,a_2=13,a_3=16\) \(a_{4n}=8\) for all \(n\) \(a_{4n+1}=4\) for \(n\geq 1\) \(a_{4n+2}=2\) for \(n\geq 1\) \(a_{4n+3}=5\) for \(n\geq 1\)

  20. anonymous
    • 5 years ago
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    can you make the formula for me pretty please

  21. watchmath
    • 5 years ago
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    I wrote the formula above! You need to free your mind! the formula doesn't always means that you have to write it as a single expression. The description above is count as formula too.

  22. anonymous
    • 5 years ago
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    ok i need to tell you something i am an 11 year old child in harrow that goes to Glebe Primary School my teacher gave me a sequnce and i had to find out the 500th term usin a simple formula do u think i can understand wat u just wrote

  23. anonymous
    • 5 years ago
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    at 11 you learn about sequences?? tell your teacher to relax a bit :-)

  24. anonymous
    • 5 years ago
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    i have to find a formula to be in this level six study group at school

  25. watchmath
    • 5 years ago
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    Ok, you must be smart since your teacher has a high hope for your and give you this problem. The formula that I gave above basically says that to find the nth terms of the sequence (were \(n\geq 4\) )) we do the following: When n/4 has no remainder, then the nth term is 8 when n/4 has 1 as the remainder, then the nth term is 4 when n/4 has 2 as the remainder, then the nth term is 2 when n/4 has 3 as the remainder, then then nth term is 5 For example what is the 6666th term? Lets divide 6666/4. We have 1666 with remainder 2. So the 6666th term is 2.

  26. anonymous
    • 5 years ago
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    ooooooooooooo i get it

  27. anonymous
    • 5 years ago
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    so 500/4 is 125 with no remainder so it is 8

  28. watchmath
    • 5 years ago
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    perfect!!

  29. anonymous
    • 5 years ago
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    thank u very much u are the best u should get a job as a teacher

  30. anonymous
    • 5 years ago
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    wat do u mean by remainder 6666/4=1666.5 so how is it 2

  31. watchmath
    • 5 years ago
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    \(6666=4\cdot 1666 + 2\) So the remainder is 2. You need to divide by hand to get the remainder.

  32. anonymous
    • 5 years ago
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    what is the hand

  33. watchmath
    • 5 years ago
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    By hand means not using calculator. No body teach to divide by "hand" anymore? :D

  34. anonymous
    • 5 years ago
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    how does 6666= 4.1666+2=

  35. anonymous
    • 5 years ago
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    i hav no idea where u get the remainder 2 from

  36. watchmath
    • 5 years ago
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    Do you know how to divide just using paper and pencil?

  37. anonymous
    • 5 years ago
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    yes i do

  38. watchmath
    • 5 years ago
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    Ok, try to divide 6666 by 4 using paper and pencil.

  39. anonymous
    • 5 years ago
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    ooooooo i see it now thank u very much u are the best

  40. watchmath
    • 5 years ago
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    good for you :D

  41. anonymous
    • 5 years ago
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    bye thank u so much

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