Practice Geometric Sequence in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A sequence where each term is obtained from the previous by multiplying by a fixed non-zero constant called the common ratio r.
Multiply by the same number each step — 2, 6, 18, 54, ... (multiply by 3). This is exponential growth.
Example 1
easyA geometric sequence has a_1 = 5 and r = 2. Find a_8 and S_8.
Example 2
mediumBacteria double every 3 hours. Starting with 500, how many after 15 hours?
Example 3
easyFind r and a_6 for the sequence 3, 6, 12, 24, \ldots
Example 4
hardIn a geometric sequence, a_2 = 6 and a_5 = 48. Find a_1 and r.
Example 5
mediumFind the 6th term of the geometric sequence: 2, 6, 18, ...