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.

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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.

Mathematics
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to find common difference \[\huge\rm \frac{ a_{10} -a_5 }{ 10-5 }\] difference between both terms and the number of terms
a_10 = 58 and a_5 =28 so subtract \[\huge\rm \frac{ 58-28 }{ 10-5 }\]
Ok, so you get the common difference of 6.

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yes right now we to find number of the terms use the sum formula for arithmetic\[S_n =\frac{ n(a_1 +a_n) }{ 2 }\]
and i just noticed we don't have the first term hm
yes we do- its 4
we can use the formula to find term \[\huge\rm a_n =(r)^{n-k}\]
opps sorry i was looking at the wrong page thats for geometric sequence
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
btw you can use 10th term doesn't matter u will get the same answer :=)
oh!! you already found it yes it's 4
can i see the answer for last part little confused on that part
The last part? You mean the first question that I didn't include?
`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
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
So I got help yesterday for the first one and now I m stuck on how to find the answers for (ii)
ohh i see..
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
444**
Ok I will try that quickly
try to work on it ive to go to eat something BRB
sure
Ok I also actually have to be away for a little while. Will come back to this as soon as I can.
alright tag me when u r ready :=)
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
I am back now @Nnesha , sorry for taking up so much of your time!
Anyway the quadtratic I ended up with was \[-7n^{2}+2n +888\] which looks a bit odd. Did I go wrong somewhere?
Trying to solve it now
888 ?O_*
Yeah that didn't work
I can send a picture of my working out
ohh it supposed to be a_1 `+` a_n
sorry about taht ..
What do you mean?
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
\(\color{blue}{\text{Originally Posted by}}\) @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
Oooooh ok let me try that quickly
i'll try it let's see what we get
Now the quadratic I get is \[n ^{2} + \frac{ 1 }{ 3 } -148=0\]
1/3 ? how did you get that ? o.O
Oh dear. Umm I had -6n^2 -2n +888 and I divided everything by -6
ohh so 1/3n*
Oh yes, sorry
\[n ^{2} + \frac{ 1 }{ 3 }n -148=0\] can you solve for n ?
Yup doing that now-almost done
alright let me know what you get
Ok done- the positive value I got was 12.00333333. Do I round that down to 12?
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 :=)
good job! :=)
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 :)
np & you too!

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