Finding Terms in 2, 6, 18, 54, ...

Algebra 1 · Axiom Academy

EXAMPLE Finding Terms in a Geometric Sequence Identify the common ratio, build the explicit formula, and use it to find any term in the sequence 2, 6, 18, 54, … The geometric sequence below begins Find its common ratio, write the explicit formula , and use it to find the 10th term. Nice work! You found any term of a geometric sequence using its common ratio. Remember: Geometric sequences multiply by a constant: that constant is the common ratio r . Find the common ratio: divide any term by the one before it — here . The explicit formula is : the exponent is n-1 because a_1 has been multiplied by r zero times. Use it for efficiency: , found without listing the first nine terms. This method works for any geometric sequence — change a_1 and r and the same formula does the rest.

This is the written version of the interactive lesson above. See the full Algebra 1 course.