Examples of Mathematical Sequences

Now, you’ll get to see sequences where you find the next number in the sequence by multiplying the previous number by another number, or subtracting a number from the previous number.

Example 1

The sequence

1,2,4,8,16,… ⁡

has the property that you multiply the previous number by 2 to find the next number:

1 ⋅ 2 = 2, the first number of the sequence multiplied by 2 is the second number of the sequence.

2 ⋅ 2 = 4, the second number of the sequence multiplied by 2 is the third number of the sequence.

4 ⋅ 2 = 8, the third number of the sequence multiplied by 2 is the fourth number of the sequence.

8 ⋅ 2 = 16, the fourth number of the sequence multiplied by 2 is the fifth number of the sequence.

16 ⋅ 2 = 32, the fifth number of the sequence multiplied by 2 is the sixth number of the sequence.

The second through to the sixth number of the sequence

Example 2

The sequence

40,35,30,25,20,… ⁡

has the property that 5 is subtracted from the previous number in the sequence to get the next number in the sequence:

40 − 5 = 35, the first number of the sequence minus 5 is the second number of the sequence.

35 − 5 = 30, the second number of the sequence minus 5 is the third number of the sequence.

30 − 5 = 25, the third number of the sequence minus 5 is the fourth number of the sequence.

25 − 5 = 20, the fourth number of the sequence minus 5 is the fifth number of the sequence.

20 − 5 = 15, the fifth number of the sequence minus 5 is the sixth number of the sequence.

The nine first numbers of the sequence

Think About This

Are there sequences where you find the next number by dividing by a specific number?

Yes, there are. An example of this is the sequence

192,96,48,24,12,6,3,… ⁡

The pattern here is that each number in the sequence is the previous number divided by 2. 192 : 2 = 96, the first number of the sequence divided by 2 is the second number of the sequence.