Question

Is the set of numbers one 1,5,25 and 125 a geometric sequence

Answer 1

Short answer: Yes.
Each member of the sequence is multiplied by 5 to get to the next member of the sequence.

Find the general equation.
tn = a*5^(n - 1)

Example
t4 = 1*5^(4 - 1)
t4 = 1*5^3
t4 = 125 just as the sequence shows.

t5 = 1^5^4
t5 = 625     Any member of the sequence can be found this way.