Let am be the number of strings (of all lengths) with digits in {1, 2, 3} (repeats allowed) such 6. that the sum of the digits in the string is equal to n. (a) Find a recurrence relation satisfied by the an (don't forget the base case(s)). (b) Use your answer to part (a) to prove that an < 2".

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Q: 7. Check that a=2" +1 is a solution to the recurrence relation an -2-1-1 with a₁ = 3. n

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Q: Write out the first six terms of the sequence defined by the recurrence relation with the given…

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