Question 1163799
.
The sum of 40 terms of a certain arithmetic sequence is 430, while the sum of 60 terms is 945. 
Determine the nth term of the arithmetic sequence.
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<pre>
The sum of any AP is the average of its extreme terms times the number of terms.

So, from the condition


    {{{((a[1]+a[40])/2)*40}}} = 430.

    {{{((a[1]+a[60])/2)*60}}} = 945.



It gives

    {{{a[1] + a[40]}}} = {{{(430*2)/40}}} = 21.5     (1)

    {{{a[1] + a[60]}}} = {{{(945*2)/60}}} = 31.5     (2)



Now subtract equation (1) from equation (2)

    {{{a[60]}}} - {{{a[40]}}} = 31.5 - 21.5 = 10.



But   {{{a[60]}}} - {{{a[40]}}} = 20d,  where "d"  is the common difference.

Hence,  d = 10/20 = 0.5.



Next,  from equation (1)

    {{{a[1]}}} + {{{a[1]+39*0.5}}} = 21.5;

hence,

    {{{a[1]}}} = {{{(21.5 - 39*0.5)/2}}} = 1.



Now the n-th term is   {{{a[n]}}} = {{{a[1]}}} + (n-1)*d = 1 + (n-1)*0.5.        <U>ANSWER</U>
</pre>

Solved.


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My lessons on arithmetic progressions in this site are

&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/Chocolate-bars-and-arithmetic-progressions.lesson>Chocolate bars 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> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Calculating-partial-sums-of-arithmetic-progressions.lesson>Calculating partial sums of arithmetic progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Finding-number-of-terms-of-an-arithmeti--progression.lesson>Finding number of terms of an arithmetic progression</A> 

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Interior-angles-of-a-polygon-and-Arithmetic-progression.lesson>Interior angles of a polygon and Arithmetic progression</A> 

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


Also, 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.