Question 160185
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a. 100, 150, 225, 337.5, 506.25...

Question: What do we have to multiply {{{u[1]=100}}} by to get {{{u[2]=150}}}?
Answer: To find out we divide 150 by 100 and get 1.5.

Question: What do we have to multiply {{{u[2]=150}}} by to get {{{u[3]=225}}}?
Answer: To find out we divide 225 by 150 and get 1.5

Question: What do we have to multiply {{{u[3]=225}}} by to get {{{u[4]=337.5}}}?
Answer: To find out we divide 337.5 by 225 and get 1.5

Question: What do we have to multiply {{{u[4]=337.5}}} by to get {{{u[5]=506.25}}}?
Answer: To find out we divide 150 by 100 and get 1.5

So we generalize:

So in each case above, what did we have to multiply {{{u[n]}}} by to get 
{{{ matrix(1,1, "u[n+1]")  }}}?
Answer: We had to multiply it by 1.5.

What did we start with?  
Answer: We started with {{{a[1]=100}}}.

So how do we write the recursive formula:

Answer:
{{{matrix(1,8,"{", u[1]=100, ",", u[n+1], " ","=", 1.5u[n], "}" )   }}}


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b. 73.4375, 29.375, 11.75, 4.7, 1.88...

Do it exactly the same way:

Answer
{{{matrix(1,8,"{", u[1]=73.4375, ",", u[n+1], " ","=", 0.4u[n], "}" )   }}}

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c. 80.00, 82.40, 84.87, 87.42, 90.04....

Do it exactly the same way, except we must always round to
the nearest hundredth:

Answer
{{{matrix(1,9,"{", u[1]=80.00, ",", u[n+1], " ","=", 1.03u[n], "rounded_to_nearest_hundredth", "}" )   }}}

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d. 208.00, 191.36, 176.05, 161.97

Same as c:

Answer
{{{matrix(1,9,"{", u[1]=208.00, ",", u[n+1], " ","=", 0.92u[n], "rounded_to_nearest_hundredth", "}" )   }}}

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Edwin</pre></b></font>