Smart Math guide · Advanced Math Ideas

Recognize Geometric Sequences

A geometric sequence changes by a constant ratio.

All levelsWorked example includedSelf-check included
The method

How to use it

  1. Divide consecutive nonzero terms to find r.
  2. Use a_n=a_1 r^(n−1).
  3. Check by repeated multiplication.
Worked example

See it in action

3,6,12,... has r=2, so a_6=3×2⁵=96.

Check your thinking

How to verify it

Terms double: 3,6,12,24,48,96.