hint Use the general solution to the homogeneous problem ab

hint: : Use the general solution to the homogeneous problem above, and then try an = A, a constant, to find particular solution.

a0 = 3, a1 = 6 and an = a n-1 + 6a n-2 + 1 for n > = 2 hint: : Use the general solution to the homogeneous problem above, and then try an = A, a constant, to find particular solution.

Solution

given,

a₀=3 , a₁=6 and n>=2

so,

a₂=a_2-1+ 6a_2-2+1=a₁ + 6a₀ + 1 =6+6*3+1=6+18+1=25

a₃ =a_3-1+ 6a_3-2+1 =a₂+ 6a₁ + 1 = 25 + 6*6 +1 =25+36+1=62

a₄=a_4-1+ 6a_4-2+1 = a₃ + 6a₂ + 1= 62+6*25+1 = 213