A sequence a1,a2,a3,… a_1, a_2, a_3, \dots\,a1,a2,a3,… is defined by
a1=qan=5an−1+3,n≥2 \begin{aligned}a_1 &= q \\a_n &= 5a_{n-1} + 3, \quad n \geq 2\end{aligned} a1an=q=5an−1+3,n≥2Find an expression for a2 a_2\,a2 in terms of qqq.
Show that a3=25q+18a_3 = 25q + 18a3=25q+18.
Find ∑r=14ar\sum_{r=1}^4 a_r∑r=14ar in terms of qqq.
