Question 1096566
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<pre>
Notice that

  {{{a[1] + a[2] + a[3] + a[4] + a[5] + a[6] + a[7] + a[8] + a[9] + a[10]}}} =

= {{{(a[1]+a[10])}}} + {{{(a[2]+a[9])}}} + {{{(a[3]+a[8])}}} + {{{(a[4]+a[7])}}} + {{{(a[5]+a[6])}}}.


Also notice that all 5 the sums in pairs are the same.

So, you actually have  {{{5*(a[5]+a[6])}}} = 240,  which implies

{{{a[5] + a[6]}}} = {{{240/5}}} = 48,  and then

{{{23 + a[6]}}} = 48,  which gives  {{{a[6]}}} = 48 - 23 = 25.


Thus the common difference is  d = {{{a[6]-a[5]}}} = 25-23 = 2.


Then  {{{a[1]}}} = {{{a[5]-4*d}}} = 23 - 4*2 = 23 - 8 = 15.


So, the progression has the first term of 15 and the common difference of 2.


Then {{{a[60]}}} = 15 + 2*59 = 133   and the sum of the first 60 terms is


{{{S[60]}}} = {{{((a[1]+a[60])/2)*60}}} = {{{((15+133)/2)*60}}} = (15+133)*30 = 4440.


<U>Answer</U>.  {{{S[60]}}} = 4440.  Option B).
</pre>


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On arithmetic progressions, see the lessons in this site:

&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>

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/One-characteristic-property-of-arithmetic-progressions.lesson>One characteristic property of arithmetic progressions</A>

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



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.