geometric sequence - a sequence where the ration of any term to the previous term is constant. common ratio - the constant ratio that is denoted by r.

a _{1} is the first term. r is the common ratio. Use only the a_{1} and r values to write the rule.

Determine the a_{1} and r values. Substitute the a_{1} and r values into a_{n} = a_{1}r^{ n-1.} The a_{1} and r values can't be multiplied because r is the base of n-1, it's not the product of a_{1} and r.

Find a_{1} by substituting the given information into a_{n} = a_{1}r^{ n-1} Substitute the a_{1} and r values only into a_{n} = a_{1}r^{ n-1} The a_{1} and r values can't be multiplied because r is the base of n-1, it's not the product of a_{1} and r.

Write a system of equations. Eq. 1: substitute one of the n values into a_{n} = a_{1}r^{ n-1}. Eq. 2: substitute the other n value into a_{n} = a_{1}r^{ n-1}. Simplify each equation. Solve one of the equations for a_{1}. Substitute this expression for a_{1} into the other equation to find r. (Solving systems by substituting.) Substitute the r value into either Eq. 1 or Eq. 2 to find a_{1}. Substitute the a_{1} and r values into a_{n} = a_{1}r^{ n-1}.