Solution.
an=8an−1−16an−2;
a) an=0?
Replace n in an=0 by n−1
an−1=0;
Replace n in an=0 by n−2
an−2=0;
8an−1−16an−2=8⋅0−16⋅0=0=an; Yes
b)an=n4?
Replase n in an=n4 by n−1
an−1=(n−1)4;
Replase n in an=n4 by n−2
an−2=(n−2)4
8(n−1)4−16(n−2)4=8(n4−4n3+6n2−4n+1)−16(n4−8n3+24n2+−32n+16)=8n4−32n3+48n2−32n+8−16n4+128n3−384n2+512n−256=−8n4+96n3−336n2+480n−248=/n4;
No
Answer: a)Yes;
b)No.
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