Question 1186207
.
A 42-year-old man was infected by a corona virus disease. The doctor advised him 
to take a 500 mg of medication on the first day and decrease the dosage by one half each day for a week. 
What is the amount of medication will he take on the 7th day? Express your answer to the nearest whole number.
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<pre>
        T           A            B             L             E
     ---------------------------------------------------------------


The day                  1       2      3       4       5       6       7   

The amount, in grams    500    500/2  500/4   500/8   500/16   500/32  500/64



Thus you have this sequence of numbers  {{{500/2^(n-1)}}},  n = 1, 2, 3, 4, 5, 6, 7.


This sequence is called "geometric progression", or, equivalently, "geometric sequence".


The amount for the 7-th day is  {{{500/2^6}}} = {{{500/64}}} = 7.81 = 8 grams (rounded).
</pre>

Solved, answered and explained.


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On geometric progressions, &nbsp;see introductory lessons

&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>

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>"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.