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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.

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