Çözüldü Limits of A Convergent Sequence and Subsequences - Quadratic Equations

If is the general term of a convergent sequence composed of positive terms, and then what is the limit of the general term?

A) 1 / 2
B) 1 / 4
C) 2
D) 4
E) -1

If the original sequence converges, all sub-sequences converge to the same limit. Therefore, all the limits of these sub-sequences and the limit of the main sequence given in the problem are the same. Let that limit be L, then L^2 - 3L - 4 = 0 ⇒ (L - 4)(L + 1) = 0 and L = 4 > 0.

Source: https://web.mat.bham.ac.uk/R.W.Kaye/seqser/subsequences2.html
Note: The question is from the 1975 Turkish University Entrance Exam that I took as well.