Question 1094753
.
The {{{highlight(cross(six))}}} sixth term of an arithmetic progression is 23 and the sum of the first six terms is 78.Find
(a)the common difference and the first term
(b)the tenth term
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<pre>
Since the sum of the six terms is 78 and the 6-th term is 23, the sum of the first 5 terms is 78-23 = 55.


In turn, it means that the 3-rd term, which is exactly in the middle of that five terms, is  {{{55/5}}} = 11.


Thus we know that {{{a[3]}}} = 11  and  {{{a[6]}}} = 23.  The difference  {{{a[6]}}} - {{{a[3]}}} =   23-11 = 12 is exactly 3 times the common difference.


Hence, the common difference is {{{12/3}}} = 4.
</pre>

Now you know ALL about this progression and can answer any question on your own.



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On arithmetic progressions, see the introductory lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson>Word problems on arithmetic progressions</A>

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic <U>"Arithmetic progressions"</U>.



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.