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
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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
@sirm3d
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
@timo86m
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 :/

Looking for something else?

Not the answer you are looking for? Search for more explanations.