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let {a

_{k}} be a sequence of real numbers. and the sequence is defined as

[tex]a_0 = 2006[/tex]

[tex]a_{n} = \log_{2}a_{n-1}[/tex]

now i have to find out the number of terms in the sequence.

this is what i have done:

i see that a

_{5}is negative. so we can't find out a

_{6}or any other subsequent terms. so the number of terms is 6 (a

_{0}upto a

_{5}).

but how can i find out the number of terms without calculating the terms upto a

_{5}? is there a way to do it?