+163 The sequence \((a_n)\) is defined by \(a_0=2, a_1=1\) and \(a_n=a_{n-1}\sqrt{3}-a_{n-2}\)
for all \(n\geq2\) Find \(a_{100}\).
Thanks in advance.
+23252 If you use the rules of the sequence, you will get the first six elements to be unique elements.
When you continue the sequence, you will find that:
a6 = -ao a7 = -a1 a8 = - a2 a9 = -a3 a10 = - a4 a11 = -a5
Continuing, you find that:
a12 = a0 a13 = a1 a14 = a2 ...
Etc.
Knowing this, can you calculate the value of a100?
