Here, the sentence talks about the 'cycle' as general class of things. Since we are referring to general things, we need to use the definite article 'a'.
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Q. There is . . . . . . . . party at Bill's house tonight.
Q. Idioms and Phrases: through his hat.
Q. Change the voice: The poet read his long poem himself.
Q. There is . . . . . . . . Kalidas in my class.
Q. . . . . . . . . weather was terrible yesterday, so we spent all day at . . . . . . . . home.
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