## 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 :/

1. anonymous

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. anonymous

terms are $-6,-6+d,-6+2d,-6+3d,-6+4d,-6+5d,-6+6d=5$ solve for $$d$$

3. anonymous

after solving d, use the same formula with n=10, a10=5, k=1 and the value of d to solve a1.

4. lilsis76

okay @sirm3d i got the a10=5 i get 2 and a4=-6 i got about -1 1/2

5. anonymous

hmm i get $-6+6d=5$ $6d=11$ $d=\frac{11}{6}$

6. 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

7. anonymous

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. anonymous

$\large n=10: av_{10} =av_1+(10-1)d$$\large n=4: av_{4}=av_1+(4-1)d$

9. lilsis76

okay i get... 5= a + 9d and -6= a+3d

10. lilsis76

@sirm3d how can i figure out the rest?

11. anonymous

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

12. anonymous

$\large \begin{matrix}5=a+9d \\ 6=-a-3d\end{matrix}$

13. lilsis76

okay i get d=11/6

14. lilsis76

@sirm3d

15. lilsis76

is there anything else to do? i think there is but i dont know what

16. lilsis76

@Outkast3r09 is there anything i gotta do next ? and how?

17. lilsis76

@timo86m

18. anonymous

now use d = 11/6 in either equation 1 or 2, then solve a $\huge 5=a+9(\frac{11}{6})$

19. lilsis76

i get -1 1/2

20. anonymous

$\large 5 - \frac{33}{2} = a$

21. anonymous

|dw:1353807088189:dw|

22. lilsis76

|dw:1353803493845:dw|i end up getting

23. anonymous

|dw:1353807189994:dw|

24. lilsis76

okay, thank you so much i see what i hav to do with fractions. i hate fractions :/