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1) Suppose a1, a2, a3, ... is a sequence of integers such that a1 =1/16 and...

1) Suppose a1, a2, a3, ... is a sequence of integers such that a1 =1/16 and an = 4an−1. Guess a formula for an and prove that your guess is correct.

2) Show that given 5 integer numbers, you can always find two of the numbers whose difference will be a multiple of 4.

3) Four cats and five mice form a row. In how many ways can they form the row if the mice are always together?

Please help me with these and provide all the work done to reach the answer.

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