iran-konkur 2021 Q109

iran-konkur · Other · konkur-riazi_1400_specialized Sequences and series, recurrence and convergence Direct term computation from recurrence
109. Suppose the general term of the logistic recurrence sequence $a_{n+1} = \dfrac{1}{a_n} + 1$ with condition $a_1 = 1$ equals $\dfrac{k}{m}$. The ninth and eighth terms of the sequence, which one is correct?
(1) $\dfrac{k-m}{2m-k}$ (2) $\dfrac{k-2m}{k-m}$ (3) $\dfrac{k-m}{k-2m}$ (4) $\dfrac{2m-k}{k-m}$
\textbf{109.} Suppose the general term of the logistic recurrence sequence $a_{n+1} = \dfrac{1}{a_n} + 1$ with condition $a_1 = 1$ equals $\dfrac{k}{m}$. The ninth and eighth terms of the sequence, which one is correct?

\medskip
(1) $\dfrac{k-m}{2m-k}$ \hfill (2) $\dfrac{k-2m}{k-m}$ \hfill (3) $\dfrac{k-m}{k-2m}$ \hfill (4) $\dfrac{2m-k}{k-m}$

\medskip