FERMAT 2001 Problem 23

A sequence t_1,t_2,\dots,t_n,\dots is defined as follows:

\begin{aligned} & t_1=14 \\ & t_k=24-5 t_{k-1}, \text { for each } k \geq 2 . \end{aligned}

For every positive integer n,t_n can be expressed as t_n=p\cdot q^n+r, where p,q and r are constants. The value of p+q+r is

Answer Choices
A. -5
B. -3
C. 3
D. 17
E. 31