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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.
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

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1to find common difference \[\huge\rm \frac{ a_{10} a_5 }{ 105 }\] difference between both terms and the number of terms

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1a_10 = 58 and a_5 =28 so subtract \[\huge\rm \frac{ 5828 }{ 105 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, so you get the common difference of 6.

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1yes right now we to find number of the terms use the sum formula for arithmetic\[S_n =\frac{ n(a_1 +a_n) }{ 2 }\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1and i just noticed we don't have the first term hm

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1we can use the formula to find term \[\huge\rm a_n =(r)^{nk}\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1opps sorry i was looking at the wrong page thats for geometric sequence

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1alright so to find 1st term \[\huge\rm a_5 = a_1 +(n1)d\] d= 6 and we are using 5th term to find first one so n would be 5 \[\huge\rm 28=a_1+(51)6\] solve for a_1

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1btw you can use 10th term doesn't matter u will get the same answer :=)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1oh!! you already found it yes it's 4

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1can i see the answer for last part little confused on that part

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The last part? You mean the first question that I didn't include?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I got help yesterday for the first one and now I m stuck on how to find the answers for (ii)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1alright so we should use \[\huge\rm s_n =\frac{ n(a_1a_n )}{ 2 }\] a_1 is 4 replace a_n with the a_1 equation which is a_1 = 4+(n1)6 then solve for n s_n=144

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok I will try that quickly

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1try to work on it ive to go to eat something BRB

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok I also actually have to be away for a little while. Will come back to this as soon as I can.

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1alright tag me when u r ready :=)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1ie found this http://math.stackexchange.com/questions/709276/arithmeticsequencefindtermgivensumoftermsa1andd you should get quadratic equation hm

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am back now @Nnesha , sorry for taking up so much of your time!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Anyway the quadtratic I ended up with was \[7n^{2}+2n +888\] which looks a bit odd. Did I go wrong somewhere?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Trying to solve it now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah that didn't work

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I can send a picture of my working out

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1ohh it supposed to be a_1 `+` a_n

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1alright so we should use \[\huge\rm444 =\frac{ n(4+(4+(n1)6 )}{ 2 }\] a_1 is 4 replace a_n with the a_1 equation which is a_1 = 4+(n1)6

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1\(\color{blue}{\text{Originally Posted by}}\) @Nnesha alright so we should use \[\huge\rm s_n =\frac{ n(a_1a_n )}{ 2 }\] a_1 is 4 replace a_n with the a_1 equation which is a_1 = 4+(n1)6 then solve for n s_n=144 \(\color{blue}{\text{End of Quote}}\) there supposed to be plus sign

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oooooh ok let me try that quickly

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1i'll try it let's see what we get

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now the quadratic I get is \[n ^{2} + \frac{ 1 }{ 3 } 148=0\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.11/3 ? how did you get that ? o.O

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh dear. Umm I had 6n^2 2n +888 and I divided everything by 6

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1\[n ^{2} + \frac{ 1 }{ 3 }n 148=0\] can you solve for n ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yup doing that nowalmost done

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1alright let me know what you get

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok done the positive value I got was 12.00333333. Do I round that down to 12?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1looks right \[ 444 =\frac{ n(8+6n6) }{ 2 } ~~~~~= \frac{ n(6n+2) }{ 2 }\] i did it differently but got same answer so i guess 12 is right :=)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you! Again I am sorry for taking up so much of your time. I really appreciate your help. Hope you have a nice day :)
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