Question 1119641
.
The problem has two solutions  (two answers).


One answer is the sequence  12, 24, 48,   found by John.


The second answer is the sequence  4, -8, 16.


<U>Solution</U>


<pre>
The three terms are  a, ar and ar^2.


From the first part of the condition ("the third term is 4 times the first term") you have

ar^2 = 4a,


which implies  r^2 = 4  and, hence,  r = +/- 2.


1)  Let r = 2.  Then you get the sequence  12, 24, 48,  as John obtained it.


2)  Let r = -2.  


    Then the second part of the condition says

    ar^2 - ar = 24  ====>  a*4 - a*(-2) = 24  ====>  6a = 24  ====>  a = 4,


    and you get the second sequence  4, -8, 16.
</pre>

Solved.