Question 1181078
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find the common ratio, explicit formula, and the recursive formula
a4 = -1/4 and a1 = 2
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<pre>
    {{{a[4]}}} = {{{a[1]*r^3}}}


    {{{-1/4}}} = {{{2*r^3}}}


    {{{r^3}}} = {{{((-1/4))/2}}} = {{{-1/8}}}


    r = {{{root(3,-1/8)}}} = {{{-1/2}}}.    (the common ratio).             <U>ANSWER</U>


Recursive formula  {{{a[n+1]}}} = {{{(-1/2)*a[n]}}}.                    <U>ANSWER</U>


Explicit formula   {{{a[n]}}} = {{{2*(-1/2)^(n-1)}}} = {{{(-1)^(n-1)/2^(n-2)}}}.     <U>ANSWER</U>
</pre>

Solved.