Question

If a1= 7 and an= -4an-1 + 5 then find the value of a4.

Answer 1

Given that

$\begin{gathered} a_1=7 \\ a_{_{}n}=-4a_{n-1_{}}+5 \end{gathered}$

Hence,

$\begin{gathered} a_2=-4a_1+5 \\ =-4(7)+5 \\ -28+5=-23 \end{gathered}$

Similarly,

$\begin{gathered} a_3=-4a_2+5 \\ a_3=-4(-23)+5 \\ =92+5=97 \end{gathered}$

Therefore,

$\begin{gathered} a_4=-4a_3+5 \\ a_4=-4(97)+5 \\ =-388+5 \\ =-383 \\ \\ a_4=-383 \end{gathered}$