Problem 7: Linear Homogenous Recurrences Consider the "Retirement Series", so named because the coefficients of its recurrence correspond to the "standard" retirement age of 65 : R(0)=0,R(1)=1,R(n)=6R(n1)5R(n2)forn>1 [a] Explain why the recurrence is considered to be "linear homogeneous". [b] State the characteristic equation of the recurrence [c] Using the methods of our course, derive a closed-form formula for R(n). [d] For the case n=2, test your formula for R(n) against the original recurrence. Problem 7: Linear Homogenous Recurrences Consider the "Retirement Series", so named because the coefficients of its recurrence correspond to the "standard" retirement age of 65 : R(0)=0,R(1)=1,R(n)=6R(n1)5R(n2)forn>1 [a] Explain why the recurrence is considered to be "linear homogeneous". [b] State the characteristic equation of the recurrence [c] Using the methods of our course, derive a closed-form formula for R(n). [d] For the case n=2, test your formula for R(n) against the original recurrence