The next term in the geometric sequence 4, 8, 16 is 32.
Understanding Geometric Sequences
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Calculating the Common Ratio
To find the common ratio in the sequence 4, 8, 16, we can divide any term by its preceding term:
- 8 / 4 = 2
- 16 / 8 = 2
So, the common ratio is 2.
Finding the Next Term
To find the next term in the sequence, we multiply the last term (16) by the common ratio (2):
- 16 * 2 = 32
Example of a Geometric Sequence
As the reference shows, an example of a geometric sequence is 2, 4, 8, 16, 32, 64... Here the common ratio is also 2. This clearly demonstrates how each term is generated by multiplying the previous term by the common ratio.
Summary
In the sequence 4, 8, 16, the common ratio is 2. Multiplying 16 by 2 gives us the next term, which is 32. This follows the definition of a geometric sequence, as seen in our example from the provided reference.
