True
A linear recurrence relation involving a sequence of numbers [tex]a_n[/tex] is one of the form
[tex]\displaystyle\sum_{k=0}^nc_{n-k}a_{n-k}=c_na_n+c_{n-1}a_{n-1}+\cdots+c_2a_2+c_1a_1=c[/tex]
where [tex]c_1,c_2,\ldots,c_n[/tex] and [tex]c[/tex] are any fixed numbers.
The given recurrence can be rearranged as
[tex]a_n=a_{n-1}+2\implies 1\cdot a_n+(-1)\cdot a_{n-1}=2[/tex]
A nonlinear recurrence would have a more "exotic" form that cannot be written in the form above. Some example:
[tex]a_n+\dfrac1{a_{n-1}}=1[/tex]
[tex]a_na_{n-1}=\pi[/tex]
[tex]{a_n}^2+\sqrt{a_{n-1}}-\left(\dfrac{a_{n-2}}{\sqrt{a_n}}\right)^{a_{n-3}}=0[/tex]
