## lavalava Group Title The fourth term of an arithmetic sequence is 141, and the seventh term is 132. The first term is _____. 11 months ago 11 months ago

1. satellite73 Group Title

$a, a+d,a+2d,a+3d,a+4d,...$ you got $$a+3d=141$$ and $$a+6d=132$$

2. satellite73 Group Title

that means $$132-141=(a+6d)-(a+3d)=3d=-9$$ and so $$d=-3$$

3. lavalava Group Title

okay so then d=4?

4. satellite73 Group Title

actually $$d=-3$$

5. lavalava Group Title

6. satellite73 Group Title

k lets go slow

7. lavalava Group Title

8. satellite73 Group Title

actually before we even start, since $$132<141$$ is it clear that the terms are getting smaller?

9. satellite73 Group Title

in other words, "$$d$$" the "common difference" must be negative right?

10. lavalava Group Title

okay

11. satellite73 Group Title

if we call the first term $$a$$ then the second term is $$a+d$$ for some $$d$$ and the third term is $$a+2d$$, the fourth term is $$a+3d$$ the fifth term is $$a+4d$$ etc

12. satellite73 Group Title

in other words, you keep adding $$d$$ to each term to get the next term, with the sophistication that you might be "adding" a negative number

13. lavalava Group Title

okay

14. satellite73 Group Title

The fourth term of an arithmetic sequence is 141 tells you that $$a+3d=141$$

15. lavalava Group Title

okay

16. satellite73 Group Title

you see that it is the fourth term, so it is $$a+3d$$ not $$a+4d$$

17. lavalava Group Title

ohhh

18. satellite73 Group Title

and the seventh term is 132 means $a+6d=132$

19. satellite73 Group Title

from these two pieced of information we can solve for $$d$$ and then solve for $$a$$

20. satellite73 Group Title

*pieces

21. lavalava Group Title

okay

22. satellite73 Group Title

a bit of algebra shows that $a+6d-(a+3d)=3d$ right?

23. lavalava Group Title

ohh okay i get it..

24. satellite73 Group Title

so we see that $3d=132-141=-9$

25. lavalava Group Title

mhm

26. satellite73 Group Title

so far so good?

27. lavalava Group Title

and so since it is 7-4= 3 then -9/3 would be -3 right? giving us the difference

28. satellite73 Group Title

yeah $$-3$$ is the difference

29. satellite73 Group Title

what you said

30. lavalava Group Title

ohhh okay!!! i get it!! :D

31. satellite73 Group Title

you are still not done though right?

32. satellite73 Group Title

33. lavalava Group Title

hmm well pluggin in the difference and then your equation... a4=141 a3=141+3=144 a2=144+3=147 a1=147+3=150 so then the first term would be 150 right? i just did it backwards

34. satellite73 Group Title

yeah i guess so i would have said $$a+3\times (-3)=141$$or $a-9=141$ making $$a=150$$ your method means you understand what is going on, which is good but you certainly wouldn't want to use that if you had say $$a_{75}$$ and wanted $$a_1$$

35. lavalava Group Title

:D yay thank you!!! :D ohh okay... ill keep in mind that equation!! thank you soo much!

36. satellite73 Group Title

yw