Answer
a) This is a linear homogeneous.
b) This recurrence is not a linear but it is homogeneous.
c) This recurrence is a linear homogeneous.
d) This recurrence is a linear but not homogeneous.
e) This is not linear.
f) This is a linear homogeneous.
g) This is not a linear homogeneous
Work Step by Step
a) This is a linear homogeneous recurrence relation with constant coefficients of degree 3.
b) This recurrence is not a linear becausethe right-hand side is not a sum of previous terms of the sequence each multiplied by a function of $n$.
c) This recurrence is a linear homogeneous recurrence relation with constant coefficients of degree 4.
d) This recurrence is not homogeneous because there are number 2.
e) 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 $n$.
f) This is a linear homogeneous recurrence relation with constant coefficients of degree 2.
g) 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 $n$
And this is not not homogeneous because there are not terms occur that are multiples of the $a_js$
