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

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

   Step (a):

   $t\left(1\right) = 4\left(5\right)^{1}$
   $t\left(2\right) = 4\left(5\right)^{2}$
   . . .

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

   Step 1 (b):

   $4\left(5\right)^{n} = 312500$

   $5^{n} = 78125$

   Hint (b):

   How many factors of $5$ can go into $78125$?

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

   Hint (c):

   Follow the steps from part (b).

   Answer (c):

   No, because solving the equation $94500 = 4\left(5\right)^{n}$ does not result in a positive integer.