For each recurrence relation below indicate either which case of the master theorem applies, or else answer that the master theorem does not apply.

consider the recurrence relation An = 2An-1 + 8an-2 with first two terms a0 = 4 and a1 = 8. a.) write out the first five terms of the sequence defined by the recurrence relation?   b.) solve the recurrence relation.That is, find a closed formula for an.

12.) Solve the recurrence relation an = 2an-1-an-2. (a) What is the solution if the initial terms are ao = 1 and a₁ = 2? (b) What do the initial terms need to be in order for ag = 30? (c) For which x are there initial terms which make ag = x? (13. Consider the recurrence relation an = 4an-1-4an-2. (a) Find the general solution to the recurrence relation (beware the repeated root). (b) Find the solution when ao = 1 and a₁ = 2. (c) Find the solution when ao = 1 and a₁ = 8.

An= -An-1+12An-2; A0=2; A1=16 Solve the recurrence relation using the Characteristics Equation method and calculate A3 .

Determine which of these relations are reflexive. The variables x,y,x',y' represent integers. A. x~y if and only if x+y is even B. x~y if and only if x+y is odd C. x~y if and only if x+y is positive D. x~y if and only if xy is positive E. x~y if and only if x-y is a multiple of 10

LL

You borrow $500 and agree to repay $600 in two weeks, after two weeks the interest is 10% per week. if you make no payments: List the amount due for the first 10 weeks Show the recurrence relation Develop a closed form solution Prove the closed form matches the recurrence relation for at least 10 iterations

Use the substitution method to identify the big-Oh of the represented by the following recurrence relation. Note: c is a constant. T(n) = cn + T(n/2) + T(n/2), T(1) = c