Geometric Sequence Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Find rr and a6a_6 for the sequence 3,6,12,24,…3, 6, 12, 24, \ldots

Solution

  1. 1
    r=6/3=2r = 6/3 = 2.
  2. 2
    a6=3⋅25=96a_6 = 3 \cdot 2^5 = 96.

Answer

r=2r = 2; a6=96a_6 = 96
Divide any consecutive pair to find rr, then apply an=a1rn−1a_n = a_1 r^{n-1}.

About Geometric Sequence

A sequence where each term is obtained from the previous by multiplying by a fixed non-zero constant called the common ratio rr.

Learn more about Geometric Sequence →

More Geometric Sequence Examples

Example 1 easy

A geometric sequence has [formula] and [formula]. Find [formula] and [formula].

Example 2 medium

Bacteria double every 3 hours. Starting with 500, how many after 15 hours?

Example 4 hard

In a geometric sequence, [formula] and [formula]. Find [formula] and [formula].

Example 5 medium

Find the 6th term of the geometric sequence: 2, 6, 18, ...

← All Geometric Sequence Examples Geometric Sequence Concept