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lilsis76

  • 2 years ago

arithmetic sequcences and series the fourth term is an arithmetic sequcence -6, and the 10th term is 5. find the common difference and the first term. how do i go about doing this? i tried so many numbers and the closest thing i got was 1/2 for the common difference :/

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  1. sirm3d
    • 2 years ago
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    try this formula for an arithmetic sequence: \[\large a_n-a_k=d(n-k)\] use n=10, k=4, a10=5 and a4=-6 to solve the common difference

  2. satellite73
    • 2 years ago
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    terms are \[-6,-6+d,-6+2d,-6+3d,-6+4d,-6+5d,-6+6d=5\] solve for \(d\)

  3. sirm3d
    • 2 years ago
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    after solving d, use the same formula with n=10, a10=5, k=1 and the value of d to solve a1.

  4. lilsis76
    • 2 years ago
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    okay @sirm3d i got the a10=5 i get 2 and a4=-6 i got about -1 1/2

  5. satellite73
    • 2 years ago
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    hmm i get \[-6+6d=5\] \[6d=11\] \[d=\frac{11}{6}\]

  6. lilsis76
    • 2 years ago
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    wait, what is the formula i should be using? i have this one but i dont know how to use it: avn = av1 + (n - 1)d

  7. sirm3d
    • 2 years ago
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    you can also use that formula. take n=10 and av10=5 and you'll have two unknowns av1 and d use k=4 and av4=-6 and you'll get another equation in av1 and d.

  8. sirm3d
    • 2 years ago
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    \[\large n=10: av_{10} =av_1+(10-1)d\]\[\large n=4: av_{4}=av_1+(4-1)d\]

  9. lilsis76
    • 2 years ago
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    okay i get... 5= a + 9d and -6= a+3d

  10. lilsis76
    • 2 years ago
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    @sirm3d how can i figure out the rest?

  11. sirm3d
    • 2 years ago
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    multiply the second equation by (-1) then add it to the first equation. that should eliminate a and leave d to be solved.

  12. sirm3d
    • 2 years ago
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    \[\large \begin{matrix}5=a+9d \\ 6=-a-3d\end{matrix}\]

  13. lilsis76
    • 2 years ago
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    okay i get d=11/6

  14. lilsis76
    • 2 years ago
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    @sirm3d

  15. lilsis76
    • 2 years ago
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    is there anything else to do? i think there is but i dont know what

  16. lilsis76
    • 2 years ago
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    @Outkast3r09 is there anything i gotta do next ? and how?

  17. lilsis76
    • 2 years ago
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    @timo86m

  18. sirm3d
    • 2 years ago
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    now use d = 11/6 in either equation 1 or 2, then solve a \[\huge 5=a+9(\frac{11}{6})\]

  19. lilsis76
    • 2 years ago
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    i get -1 1/2

  20. sirm3d
    • 2 years ago
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    \[\large 5 - \frac{33}{2} = a\]

  21. sirm3d
    • 2 years ago
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    |dw:1353807088189:dw|

  22. lilsis76
    • 2 years ago
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    |dw:1353803493845:dw|i end up getting

  23. sirm3d
    • 2 years ago
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    |dw:1353807189994:dw|

  24. lilsis76
    • 2 years ago
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    okay, thank you so much i see what i hav to do with fractions. i hate fractions :/

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