Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

lavalava

  • one year ago

The fourth term of an arithmetic sequence is 141, and the seventh term is 132. The first term is _____.

  • This Question is Closed
  1. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[a, a+d,a+2d,a+3d,a+4d,...\] you got \(a+3d=141\) and \(a+6d=132\)

  2. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  3. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay so then d=4?

  4. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    actually \(d=-3\)

  5. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    umm please explain!!

  6. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    k lets go slow

  7. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    please and thanks

  8. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  9. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    in other words, "\(d\)" the "common difference" must be negative right?

  10. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay

  11. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay

  14. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  15. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay

  16. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  17. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ohhh

  18. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and the seventh term is 132 means \[a+6d=132\]

  19. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    from these two pieced of information we can solve for \(d\) and then solve for \(a\)

  20. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    *pieces

  21. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay

  22. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  23. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ohh okay i get it..

  24. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so we see that \[3d=132-141=-9\]

  25. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    mhm

  26. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so far so good?

  27. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  28. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah \(-3\) is the difference

  29. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what you said

  30. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  31. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you are still not done though right?

  32. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    your question asked "The first term is _____"

  33. lavalava
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  36. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.