A sequence has $a_1=-2$ and $a_2=4$ and in the sequence, when $n>2$, $a_{n}$= $\dfrac {a_{n-1}}{a_{n-2}}$. Find the sum of the first $99$ terms of sequence.
I tried to deduce from the patterns produced but couldn't draw any fruitful conclusions. $a_3=-2$, $a_4=-0.5$, $a_5=0.25$ and so on…
Best Answer
HINT
We have that
$$a_{n}= \frac {a_{n-1}}{a_{n-2}}=\frac {a_{n-2}}{a_{n-3}}\frac {1}{a_{n-2}}=\frac {1}{a_{n-3}}=\ldots=a_{n-6}$$