A theatre group is preparing rhythmic backgroud music using \(1\)-beat and \(2\)-beat syllables. The music director explains Virahanka's principle, where the number rhythms for \(n\) beats is obtained by adding the numbers of rhythms for the previous two beat lengths. The students know that rhythm \((5) = 8\), rhythm \((6) = 13\). Using this pattern, they find: rhythm \((7)\) \(=\) \(21\), rhythm \((8)\) \(=\) \(34\). The group now wants to determine the number of possible rhythms for 9 and 11 beats without listing all the possible combinations. They also want to compare the number of rhythmic patterns for the given beat lengths and identify their parity.
Answer the following questions:
(a) Find the number of possible rhythms for 9 beats.
(b) Find the number of possible rhythms for 11 beats.
(c) Find the number of possible rhythms for 13 beats.
(d) State the parity of the number of rhythms for 13 beats.