Answer
a)is a solution
b)is not a solution
c)is not a solution
d)is a solution
e)is a solution
f)is a solution
g)is not a solution
h)is not a solution
Work Step by Step
a)by substituting with a(n)=0
8(0)-16(0)=0
thus, a(n)=0 is a solution
b)by substituting with a(n)=1
8(1)-16(1)=-8
thus, a_{n} =1 is not a solution
c)by substituting with a_{n} =2^{n}
8(2^{n-1})-16(2^{n-2}) -->2^{n}(0) \ne 2^{n}
thus, a_{n}=2^{n} is not a solution
d)by substituting with a_{n} =4^{n}
4^{n}(8*4^{-1}-16*4^{-2})=4^{n}
thus, is a solution
e)by substituting with a_{n} =n4^{n}
4^{n-2}(8(n-1)*4-16(n-2))=4^{n-2}(32n-32-16n+32)=4^{n-2}(16n)=4^{n-2}*4^{-2}n
=n4^{n}
thus, it is a solution
f) substituting with a_{n}
4^{n}(4+(6n-6)-(2+3n-6)=4^{n}(3n+2)=24^{n}+3n4^{n}
g)substituting with a_{n}
(-4)^{n}(8/4 -16/16) =-3(-4)^{n}
thus, it is not a solution
h)substituting with a_{n}
4^{n}((8(n-1)^{2})/4 - (16(n-2)^{2})/16 )=4^{n}(2(n^{2} -2n +1) - (n^{2} -4n +4)
4^{n}(2n^{2} -4n +2-n^{2} +4n -4)=4^{n}(n^{2} -2)
thus , it is not a solution
