Answer :
apparently k=6. It doesn't say it in the question, but I'll assume that you had a mistype and forgot to say that the second term is 12.
Anyway,
The nth term of a geometric sequence is [tex] a_{1}* k^{n-1} [/tex]. Thus, the 52nd term would be [tex]2* k^{51} [/tex] and the 50th term would be [tex]2* k^{49} [/tex] When you divide the two, the 2's would cancel out and k^49 would cancel out, leaving you with 1 on the bottom and k^2 on the top. As we said at the beginning, k=6, so our answer is just 6*6=36.
Anyway,
The nth term of a geometric sequence is [tex] a_{1}* k^{n-1} [/tex]. Thus, the 52nd term would be [tex]2* k^{51} [/tex] and the 50th term would be [tex]2* k^{49} [/tex] When you divide the two, the 2's would cancel out and k^49 would cancel out, leaving you with 1 on the bottom and k^2 on the top. As we said at the beginning, k=6, so our answer is just 6*6=36.
The terms are: 2*k^0, 2*k ,2*k^2.....2*k^49,2*k^50,2*k^51,.....
the fifty term is 2*k^49
the fiftysecond term is 2*k^51
2*k^51/2*k^49=2*k^49*k^2/2*k^49=k^2
We know that 2*k=12⇒ k=12:2 ⇒ k=6
⇒ k^2=36
the fifty term is 2*k^49
the fiftysecond term is 2*k^51
2*k^51/2*k^49=2*k^49*k^2/2*k^49=k^2
We know that 2*k=12⇒ k=12:2 ⇒ k=6
⇒ k^2=36