Question 1069603
.
Three consecutive terms in an arithmetic sequence is given with a middle one x. The sum of the three terms is 30 and 
the product of the three terms is 840. Calculate the three terms
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<pre>
The terms are x-d, x and x+d, where d is the common difference.


For x, you have the equation 

(x-d) + x + (x+d) = 30,

which is equivalent to


3x = 30

and gives x = {{{30/3}}} = 10.


The second equation is 

(x-d)*x*(x+d) = 840,   or

(10 - d)*10*(10 + d) = 840,

which gives

{{{10^2 - d^2}}} = {{{840/10)}}},   or


{{{100 - d^2}}} = 84,   --->  {{{d^2}}} = 100 - 84 = 16,  --->  {{{d[1]}}} = 4,  {{{d[2]}}} = -4.


The first progression is  {6, 10, 14}.


The second progression is  {14, 10, 6}.
</pre>

There is a bunch of lessons on arithmetic progressions 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/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> 



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>.