If a1=1 and a^n=-5a^n-1+2 then find the value of a3

Question

i need a step by step explanation please

Answer 1

a1 = 1

a2 = -5a1 + 2 = -5+2 = -3

a3 = -5(-3) + 2 = 15+2 = 17

an = -5an-1 + 2

if n=2 then n-1 = 1, then

a2 =-5(1) + 2 = -5+2 =-3

then plug -3 into the next formula

a3 =-5(a2) + 2

a3 =-5(-3) + 2 = 15+2 = 17