Eniki has a sequence of numbers given by the formula $t\left(n\right) = 4\left(5^{n}\right)$.

1. What are the first three terms of Eniki's sequence?

   Hint (a):

   Substitute $n = 1$, $2$, $3$ into the formula.

2. Chelita thinks the number $312,500$ is a term in Eniki's sequence. Is she correct? Justify your answer by either giving the term number or explaining why it is not in the sequence.

   Hint (b):

   Let $t\left(n\right) = 312,500$ and solve for $n$. Be sure to divide both sides of the equation by $4$ before taking the log of both sides.

   What kinds of numbers will tell you if it is in the sequence?

3. Elisa thinks the number $94,500$ is a term in Eniki's sequence. Is she correct? Explain.

   Hint (c):

   See part (b).