0 votes 0 votes Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n-1}$+$2^n$ in the book solution is given $a_n$=$-2^{n+1}$ but I’m getting $a_n$=$3^{n+1}-2^{n+1}$ Combinatory kenneth-rosen discrete-mathematics recurrence-relation + – aditi19 asked May 13, 2019 edited May 13, 2019 by aditi19 aditi19 628 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply ankitgupta.1729 commented May 13, 2019 reply Follow Share what is the base condition ? $-2^{n+1}$ is the particular solution.. 0 votes 0 votes aditi19 commented May 14, 2019 reply Follow Share base condition is $a_0$=1 im getting the same homogeneous part i got $3^{n+1}$ and particular part $-2^{n+1}$ 1 votes 1 votes ankitgupta.1729 commented May 14, 2019 reply Follow Share @aditi19 your answer is correct. You can verify yourself by taking small values of 'n'. For eg., for $n=1$, recurrence relation gives $a_1=3a_0+2^1=3*1+2=5$ Now,$-2^{n+1}$ will give answer as $-2^2=-4$ where as $3^{n+1}-2^{n+1}$ will give answer as $3^2-2^2=5$. So, your answer is correct. 1 votes 1 votes Please log in or register to add a comment.