lilsis76
  • lilsis76
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 :/
Mathematics
katieb
  • katieb
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sirm3d
  • sirm3d
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
anonymous
  • anonymous
terms are \[-6,-6+d,-6+2d,-6+3d,-6+4d,-6+5d,-6+6d=5\] solve for \(d\)
sirm3d
  • sirm3d
after solving d, use the same formula with n=10, a10=5, k=1 and the value of d to solve a1.

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lilsis76
  • lilsis76
okay @sirm3d i got the a10=5 i get 2 and a4=-6 i got about -1 1/2
anonymous
  • anonymous
hmm i get \[-6+6d=5\] \[6d=11\] \[d=\frac{11}{6}\]
lilsis76
  • lilsis76
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
sirm3d
  • sirm3d
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.
sirm3d
  • sirm3d
\[\large n=10: av_{10} =av_1+(10-1)d\]\[\large n=4: av_{4}=av_1+(4-1)d\]
lilsis76
  • lilsis76
okay i get... 5= a + 9d and -6= a+3d
lilsis76
  • lilsis76
@sirm3d how can i figure out the rest?
sirm3d
  • sirm3d
multiply the second equation by (-1) then add it to the first equation. that should eliminate a and leave d to be solved.
sirm3d
  • sirm3d
\[\large \begin{matrix}5=a+9d \\ 6=-a-3d\end{matrix}\]
lilsis76
  • lilsis76
okay i get d=11/6
lilsis76
  • lilsis76
lilsis76
  • lilsis76
is there anything else to do? i think there is but i dont know what
lilsis76
  • lilsis76
@Outkast3r09 is there anything i gotta do next ? and how?
lilsis76
  • lilsis76
sirm3d
  • sirm3d
now use d = 11/6 in either equation 1 or 2, then solve a \[\huge 5=a+9(\frac{11}{6})\]
lilsis76
  • lilsis76
i get -1 1/2
sirm3d
  • sirm3d
\[\large 5 - \frac{33}{2} = a\]
sirm3d
  • sirm3d
|dw:1353807088189:dw|
lilsis76
  • lilsis76
|dw:1353803493845:dw|i end up getting
sirm3d
  • sirm3d
|dw:1353807189994:dw|
lilsis76
  • lilsis76
okay, thank you so much i see what i hav to do with fractions. i hate fractions :/

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