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 a 1 ∗ k n − 1 . Thus, the 52nd term would be 2 ∗ k 51 and the 50th term would be 2 ∗ k 49 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 52nd term divided by the 50th term of the geometric sequence is calculated using the formula for the nth term. Given the first term is 2 and the common ratio k is 6, we find that the ratio equals 36 . Therefore, the answer is 36.
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