Geometric Sequence Math Example 2

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Example 2

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

Solution

  1. 1
    The population doubles every 3 hours, so model it as a geometric sequence with ratio r=2r = 2.
  2. 2
    Find the number of doubling periods in 15 hours: 153=5\frac{15}{3} = 5 periods.
  3. 3
    Apply the geometric formula: a5=500⋅25=500⋅32=16,000a_5 = 500 \cdot 2^5 = 500 \cdot 32 = 16{,}000

Answer

16,000 bacteria16{,}000 \text{ bacteria}
Each 3-hour period multiplies the count by 2, producing a geometric sequence. After 5 periods the population reaches 16,000.

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 3 easy

Find [formula] and [formula] for the sequence [formula]

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