Consider the following recurrence relation and initial conditions.

tk$=14$tk$149$tk$2,$ for each integer$$k$2$t$0=1,$t$1=7$

$($a$)$

Suppose a sequence of the form$$

$1,$t$,$t$2,$t$3,,$tn$,$

$$where$$

t$0,$

$$satisfies the given recurrence relation $($but not necessarily the initial conditions$).$ What is the characteristic equation of the recurrence relation?

t$214$t$+49$

$$

$$