Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 8 Marks

Year: May 2016

The characteristic equation of the recurrence relation is $r^2 -7r +10 = 0$

Its roots are r= 2 and r= 5. Hence the sequence {an} is a solution to the recurrence relation if and only if

$a_n = α_1 2^n + α_2 5^n$

for some constant $α_1$ and $α_2$.

From the initial condition, it follows that

$a_0 = 1 = α_1 + α_2$

$a_1 = 6 =2α_1 + 5α_2$. Solving the equations, we get $α1= - (1/3), α2 = 4/3$ Hence the solution is the sequence {an} with an = $(-1/3). 2^n + (4/3) 5^n$.