Complete a geometric number sequence

Key Notes :

Definition of a Geometric Sequence:

  • A geometric sequence is a series of numbers where each term after the first is obtained by multiplying the previous term by a constant number called the common ratio.

Identifying the Common Ratio:

  • To find the common ratio, divide any term in the sequence by the previous term.
    Example: If the sequence is 2, 4, 8, 16, the common ratio is 42 = 2 .

Extending the Sequence:

  • Multiply the last known term by the common ratio to find the next term.
    Example: If the sequence is 3, 6, 12, 24, and the common ratio is 2, the next term is 24 × 2 = 48.

Filling in Missing Terms:

Use the common ratio to calculate the missing terms in the sequence.
Example: For the sequence 5, __, 20, __, 80 (common ratio = 4):

  • Second term = 5 × 4 = 20 ,
  • Fourth term = 20 × 4 = 80 .

Working Backward:

  • To find previous terms, divide the known term by the common ratio.
    Example: For a sequence where the third term is 27 and the ratio is 3, the second term is 27/3 = 9 .

Applications in Real Life:

  • Geometric sequences are used to model exponential growth or decay, such as population growth, interest rates, and patterns in nature.

Key Vocabulary:

  • Term: A number in the sequence.
  • Common Ratio: The number multiplied to get the next term.
  • Sequence: An ordered list of numbers.

Learn with an example

1) Type the missing number in this sequence:

5,    25,  _____  ,    625,    3,125

First, look for a pattern. Notice how each number is 5 times the previous number:

5,    25,    __,    625,    3,125

Multiply 25 by 5 to find the missing number:

25 × 5 = 125

To make the pattern complete, the number 125 must go in the blank space.

2) Type the missing number in this sequence:

2,    4,   _____ ,    16,    32,    64

First, look for a pattern. Notice how each number is 2 times the previous number:

2,    4,    __,    16,    32,    64

Multiply 4 by 2 to find the missing number:

4 × 2 = 8

To make the pattern complete, the number 8 must go in the blank space.

3) Type the missing number in this sequence:

2,    4,    8,  ____,    32,    64

First, look for a pattern. Notice how each number is 2 times the previous number:

2,    4,    8,    __,    32,    64

Multiply 8 by 2 to find the missing number:

8 × 2 = 16

To make the pattern complete, the number 16 must go in the blank space.

Let’s practice!🖊️