Question 1189826
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(a) the first term of a G.P is x and 3rd term is y. find an expression for the common ratio in terms of x and y. 

(b) the 1st and 3rd term of a G.P are 8 and 18 respectively and the common ratio is positive, find the common ratio
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                        Part (a)



<pre>
    {{{a[1]}}} = x;   {{{a[3]}}} = y = {{{a[1]*r^2}}}.


    So,  y = x*r^2,  which gives  for the common ratio  r = +/- {{{sqrt(y/x)}}}.      <U>ANSWER</U>



    Notice that this formula for the common ratio "r" works in real numbers  <U>IF and only IF</U>  

    the ratio  {{{y/x}}} is non-negative, which means that both x and y must be of the same sign, and both are not zero.
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part (b)



<pre>
    {{{a[1]}}} = 8;   {{{a[3]}}} = 18 = {{{a[1]*r^2}}} = {{{8*r^2}}}.


    It gives  r = {{{sqrt(18/8)}}} = {{{sqrt(9/4)}}} = +/- {{{3/2}}}.      


    Since the condition says that common ratio is positive, 

    it leaves only one option for the common ratio  r = {{{3/2}}} = 1.5.   <U>ANSWER</U>
</pre>

Solved.