Answer: k = -12
The mixed number -1 & 1/3 converts to the improper fraction -4/3
Let r be the common ratio. To go from one term to the next, we multiply by this common ratio. So,
second term = (first term)*(common ratio)
4 = (-4/3)*r
3*4 = 3*(-4/3)*r
12 = -4r
-4r = 12
r = -3
We multiply each term by -3 to get the next term. The third term is therefore,
third term = (second term)*(common ratio)
third term = 4*r
third term = 4*(-3)
third term = -12
and if we keep going...
fourth term = (third term)*(common ratio)
fourth term = -12*(-3)
fourth term = 36
So it matches up
If a, b, c are the geometric sequence, then
[tex]ac=b^2[/tex]
We have a = 4, b = k, c = 36. Substitute:
[tex](4)(36)=k^2\\\\k^2=144\to k=\pm\sqrt{144}\to k=-12\ \vee\ k=12[/tex]
First term is negative, therefore it's the alternating sequence. Therefore your answer is
