Answer:
[tex]h_{n}=1.(8)^{n-1}[/tex] will be the correct formula for the given sequence.
Step-by-step explanation:
The given sequence is 1, 8, 64, 512...........
The given sequence is a geometric sequence having a common ratio (r) of
r = [tex]\frac{\text{Second term}}{\text{First term}}[/tex]
r = [tex]\frac{8}{1}=8[/tex]
Since explicit formula of a geometric sequence is given by
[tex]T_{n}=a(r)^{n-1}[/tex]
where [tex]T_{n}[/tex] = nth term of the sequence
a = first term of the sequence
r = common ratio of the successive term to the previous term
Now we plug values of a and r in the formula to get the explicit formula for the given sequence.
[tex]T_{n}=1.(8)^{n-1}[/tex]
Therefore, if Bernardo is saying that the formula of the sequence is
h(n) = [tex]1.(8)^{n-1}[/tex] then he is correct.
