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lilsis76
 3 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 :/
lilsis76
 3 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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sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2try 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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0terms are \[6,6+d,6+2d,6+3d,6+4d,6+5d,6+6d=5\] solve for \(d\)

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2after solving d, use the same formula with n=10, a10=5, k=1 and the value of d to solve a1.

lilsis76
 3 years ago
Best ResponseYou've already chosen the best response.0okay @sirm3d i got the a10=5 i get 2 and a4=6 i got about 1 1/2

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0hmm i get \[6+6d=5\] \[6d=11\] \[d=\frac{11}{6}\]

lilsis76
 3 years ago
Best ResponseYou've already chosen the best response.0wait, 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
 3 years ago
Best ResponseYou've already chosen the best response.2you 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
 3 years ago
Best ResponseYou've already chosen the best response.2\[\large n=10: av_{10} =av_1+(101)d\]\[\large n=4: av_{4}=av_1+(41)d\]

lilsis76
 3 years ago
Best ResponseYou've already chosen the best response.0okay i get... 5= a + 9d and 6= a+3d

lilsis76
 3 years ago
Best ResponseYou've already chosen the best response.0@sirm3d how can i figure out the rest?

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2multiply the second equation by (1) then add it to the first equation. that should eliminate a and leave d to be solved.

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2\[\large \begin{matrix}5=a+9d \\ 6=a3d\end{matrix}\]

lilsis76
 3 years ago
Best ResponseYou've already chosen the best response.0is there anything else to do? i think there is but i dont know what

lilsis76
 3 years ago
Best ResponseYou've already chosen the best response.0@Outkast3r09 is there anything i gotta do next ? and how?

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2now use d = 11/6 in either equation 1 or 2, then solve a \[\huge 5=a+9(\frac{11}{6})\]

sirm3d
 3 years ago
Best ResponseYou've already chosen the best response.2\[\large 5  \frac{33}{2} = a\]

lilsis76
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1353803493845:dwi end up getting

lilsis76
 3 years ago
Best ResponseYou've already chosen the best response.0okay, thank you so much i see what i hav to do with fractions. i hate fractions :/
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