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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 :/
 one year ago
 one year 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 :/
 one year ago
 one year ago

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sirm3dBest ResponseYou've already chosen the best response.2
try this formula for an arithmetic sequence: \[\large a_na_k=d(nk)\] use n=10, k=4, a10=5 and a4=6 to solve the common difference
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
terms are \[6,6+d,6+2d,6+3d,6+4d,6+5d,6+6d=5\] solve for \(d\)
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
after solving d, use the same formula with n=10, a10=5, k=1 and the value of d to solve a1.
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay @sirm3d i got the a10=5 i get 2 and a4=6 i got about 1 1/2
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
hmm i get \[6+6d=5\] \[6d=11\] \[d=\frac{11}{6}\]
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
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
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
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.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
\[\large n=10: av_{10} =av_1+(101)d\]\[\large n=4: av_{4}=av_1+(41)d\]
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay i get... 5= a + 9d and 6= a+3d
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
@sirm3d how can i figure out the rest?
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
multiply the second equation by (1) then add it to the first equation. that should eliminate a and leave d to be solved.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
\[\large \begin{matrix}5=a+9d \\ 6=a3d\end{matrix}\]
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
is there anything else to do? i think there is but i dont know what
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
@Outkast3r09 is there anything i gotta do next ? and how?
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
now use d = 11/6 in either equation 1 or 2, then solve a \[\huge 5=a+9(\frac{11}{6})\]
 one year ago

sirm3dBest ResponseYou've already chosen the best response.2
\[\large 5  \frac{33}{2} = a\]
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
dw:1353803493845:dwi end up getting
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay, thank you so much i see what i hav to do with fractions. i hate fractions :/
 one year ago
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