A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

The fifth term of an arithmetic progression is 28 and the tenth term in 58. The sum of all the terms in this progression is 444. How many terms are there? In the previous question the answer shows that the first term is 4 and the common difference is 6. I also do have the answers available if needed. Please help me! I don't know what to do to answer this. If you could just set me on the right track I could try to solve it myself.

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

    to find common difference \[\huge\rm \frac{ a_{10} -a_5 }{ 10-5 }\] difference between both terms and the number of terms

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

    a_10 = 58 and a_5 =28 so subtract \[\huge\rm \frac{ 58-28 }{ 10-5 }\]

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok, so you get the common difference of 6.

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

    yes right now we to find number of the terms use the sum formula for arithmetic\[S_n =\frac{ n(a_1 +a_n) }{ 2 }\]

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

    and i just noticed we don't have the first term hm

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes we do- its 4

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

    we can use the formula to find term \[\huge\rm a_n =(r)^{n-k}\]

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

    opps sorry i was looking at the wrong page thats for geometric sequence

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

    alright so to find 1st term \[\huge\rm a_5 = a_1 +(n-1)d\] d= 6 and we are using 5th term to find first one so n would be 5 \[\huge\rm 28=a_1+(5-1)6\] solve for a_1

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

    btw you can use 10th term doesn't matter u will get the same answer :=)

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

    oh!! you already found it yes it's 4

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

    can i see the answer for last part little confused on that part

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The last part? You mean the first question that I didn't include?

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

    `How many terms are there? ` i assumed previous question was the same like this one bec we got same value for d and a_1

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The entire question is: 7. The fifth term of an arithmetic progression is 28 and the tenth term is 58 (i) Find the first term and the common difference. (ii) The sum of all the terms in this progression is 444. How many terms are there? Answers to 7. (i) common difference=6 first term=4

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So I got help yesterday for the first one and now I m stuck on how to find the answers for (ii)

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

    ohh i see..

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

    alright so we should use \[\huge\rm s_n =\frac{ n(a_1-a_n )}{ 2 }\] a_1 is 4 replace a_n with the a_1 equation which is a_1 = 4+(n-1)6 then solve for n s_n=144

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

    444**

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok I will try that quickly

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

    try to work on it ive to go to eat something BRB

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sure

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok I also actually have to be away for a little while. Will come back to this as soon as I can.

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

    alright tag me when u r ready :=)

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

    ie found this http://math.stackexchange.com/questions/709276/arithmetic-sequence-find-term-given-sum-of-terms-a1-and-d you should get quadratic equation hm

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I am back now @Nnesha , sorry for taking up so much of your time!

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Anyway the quadtratic I ended up with was \[-7n^{2}+2n +888\] which looks a bit odd. Did I go wrong somewhere?

  28. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Trying to solve it now

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

    888 ?O_*

  30. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah that didn't work

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I can send a picture of my working out

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

    ohh it supposed to be a_1 `+` a_n

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

    sorry about taht ..

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What do you mean?

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

    alright so we should use \[\huge\rm444 =\frac{ n(4+(4+(n-1)6 )}{ 2 }\] a_1 is 4 replace a_n with the a_1 equation which is a_1 = 4+(n-1)6

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

    \(\color{blue}{\text{Originally Posted by}}\) @Nnesha alright so we should use \[\huge\rm s_n =\frac{ n(a_1-a_n )}{ 2 }\] a_1 is 4 replace a_n with the a_1 equation which is a_1 = 4+(n-1)6 then solve for n s_n=144 \(\color{blue}{\text{End of Quote}}\) there supposed to be plus sign

  37. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oooooh ok let me try that quickly

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

    i'll try it let's see what we get

  39. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Now the quadratic I get is \[n ^{2} + \frac{ 1 }{ 3 } -148=0\]

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

    1/3 ? how did you get that ? o.O

  41. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh dear. Umm I had -6n^2 -2n +888 and I divided everything by -6

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

    ohh so 1/3n*

  43. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh yes, sorry

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

    \[n ^{2} + \frac{ 1 }{ 3 }n -148=0\] can you solve for n ?

  45. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yup doing that now-almost done

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

    alright let me know what you get

  47. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok done- the positive value I got was 12.00333333. Do I round that down to 12?

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

    looks right \[ 444 =\frac{ n(8+6n-6) }{ 2 } ~~~~~= \frac{ n(6n+2) }{ 2 }\] i did it differently but got same answer so i guess 12 is right :=)

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

    good job! :=)

  50. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you! Again I am sorry for taking up so much of your time. I really appreciate your help. Hope you have a nice day :)

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

    np & you too!

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.