Consider the recurrence relation an 3an-1 5n. a write the, Ask an Expert

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1. Give a recursively describe for the sequence "an" given below, including initial conditions and assume that the sequences begin with a1. an = the number of bit strings of length n that contain a pair of consecutive 0's.

2. Consider the recurrence relation an = 2an-1 + 3n. (a) Write the associated homogeneous recurrence relation. (b) Find the general solution to the associated homogeneous recurrence relation. (c) Find a particular solution to the given recurrence relation. (d) Write the general solution to the given recurrence relation. (e) Find the particular solution to the given recurrence relation when a0 = 1.

3. Consider the recurrence relation an = 3an-1 + 5n. (a) Write the associated homogeneous recurrence relation. (b) Find the general solution to the associated homogeneous recurrence relation. (c) Find a particular solution to the given recurrence relation. (d) Write the general solution to the given recurrence relation. (e) Find the particular solution to the given recurrence relation when a0 = 1.

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