Answer
a) 2,3,5,9
b) 1,4,27,256
c) 0,0,1,1
d) 0,1,2,3
Work Step by Step
a) Given: $2^n+1$
Here, $a_0=2^0+1=2; a_1=2^1+1=3;a_2=2^2+1=5;a_3=2^3+1=9$
b) Given: $(n+1)^{n+1}$
Here, $a_0=(0+1)^{0+1}=1; a_1=(1+1)^{1+1}=4;a_2=(2+1)^{2+1}=27;a_3=(3+1)^{3+1}=256$
c) Given: $⌈ n/2⌉$
$a_0=⌈ n/2⌉=0; a_1=⌈ 1/2⌉=0;a_2=⌈2/2⌉=1;a_3=⌈3/2⌉=1$
d) Given: $⌈ n/2⌉+⌈ n/2⌉$
Here, we hvae
$a_0=⌈ 0/2⌉+⌈0/2⌉=0; a_1=⌈1/2⌉+⌈1/2⌉=1;a_2=⌈2/2⌉+⌈2/2⌉=2;a_3=⌈3/2⌉+⌈3/2⌉=3$
