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Please help In the sequence below the first term is 2 and each term after the first is k times the preceding term where k is a constant. What is the value of the 52nd term divided by the 50th term?

heres the answer to this question but can someone explain more clearly how to get this answer I still don't understand the explanation given. thanks
The correct answer is 36. Since each term after the first is k times the preceding term, and 2 and 12 are the first and second terms, respectively, it follows that 2k = 12, or k = 6. Thus each term in the sequence after the first is 6 times the preceding term. Hence the 51st term of the sequence is 6 times the 50th term, and the 52nd term of the sequence is 6 times the 51st term. So if the value of the 50th term of the sequence is called x, the value of the 51st term is 6x, and the value of the 52nd term is 6(6x) = 36x. Therefore, the value of the 52nd term divided by the 50th term is 36.



Answer :

MichaelLiu
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.
dannielle
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