Question 1111732
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<pre>
{{{a[2]}}} + {{{a[3]}}} = {{{a[1]*r}}} + {{{a[1]*r^2}}} = {{{a[1]*r*(1+r)}}} = 280.       (1)


{{{a[5]}}} + {{{a[6]}}} = {{{a[1]*r^4}}} + {{{a[1]*r^5}}} = {{{a[1]*r^4*(1+r)}}} = 4375.    (2)  


Now divide eq(2) by eq(1) (both sides). After canceling common multipliers, you will get


{{{r^3}}} = {{{4375/280}}} = 15.625.


Hence,  r = {{{root(3,15.625)}}} = 2.5.


Thus the common difference is  r = 2.5.


The equation (1) the becomes

{{{a[1]*2.5*(1+2.5)}}} = 280,   which implies  {{{a[1]}}} = {{{280/(2.5*3.5)}}} = 32.


<U>Answer</U>.  The first term is 32.  The common difference is 2.5.
</pre>

Solved.


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There is a bunch of lessons on geometric progressions in this site

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

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

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

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

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

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Fresh-sweet-and-crispy-problem-on-arithmetic-and-geometric-progressions.lesson>Fresh, sweet and crispy problem on arithmetic and geometric progressions</A>

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Mathematical-induction-for-sequences-other-than-arithmetic-or-geometric.lesson>Mathematical induction for sequences other than arithmetic or geometric</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>"Geometric 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.