Answer
a) This is a linear homogeneous recurrence relation with constant coefficients of degree 2.
b) This recurrence is not homogeneous.
c) This recurrence is not linear.
d) This is a linear homogeneous recurrence relation with constant coefficients of degree 3.
e) This recurrence does not have constant coefficients.
f) This recurrence is not homogeneous.
g) This is a linear homogeneous recurrence relation with constant coefficients of degree 7.
Work Step by Step
a) This is a linear homogeneous recurrence relation with constant coefficients of degree 2 ($a_n=3a_{n-2}$ with $k=2$).
b) This recurrence is not homogeneous because there are terms occur that are multiples of the $a_js$.
c) This recurrence is not linear because the right-hand side is not a sum of previous terms of the sequence each multiplied by a function of n.
d) This is a linear homogeneous recurrence relation with constant coefficients of degree 3 ($a_n=a_{n-1}+a_{n-3}$ with $k=3$).
e) This recurrence does not have constant coefficients.
f) This recurrence is not homogeneous because there are terms occur that are multiples of the $a_js$.
g) This is a linear homogeneous recurrence relation with constant coefficients of degree 7 ($a_n=4a_{n-2}+5a_{n-4}+9a_{n-7}$ with $k=7$).
