Answer:
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 = ![\frac{\text{Second term}}{\text{First term}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BSecond%20term%7D%7D%7B%5Ctext%7BFirst%20term%7D%7D)
r = ![\frac{8}{1}=8](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B1%7D%3D8)
Since explicit formula of a geometric sequence is given by
![T_{n}=a(r)^{n-1}](https://tex.z-dn.net/?f=T_%7Bn%7D%3Da%28r%29%5E%7Bn-1%7D)
where
= 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.
![T_{n}=1.(8)^{n-1}](https://tex.z-dn.net/?f=T_%7Bn%7D%3D1.%288%29%5E%7Bn-1%7D)
Therefore, if Bernardo is saying that the formula of the sequence is
h(n) =
then he is correct.