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

$$1,\phantom{\rule{0.33em}{0ex}}2,\phantom{\rule{0.33em}{0ex}}4,\phantom{\rule{0.33em}{0ex}}8,\phantom{\rule{0.33em}{0ex}}16,\dots $$ |

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

$1\cdot 2=2$, the first number of the sequence multiplied by $2$ is the second number of the sequence.

$2\cdot 2=4$, the second number of the sequence multiplied by $2$ is the third number of the sequence.

$4\cdot 2=8$, the third number of the sequence multiplied by $2$ is the fourth number of the sequence.

$8\cdot 2=16$, the fourth number of the sequence multiplied by $2$ is the fifth number of the sequence.

$16\cdot 2=32$, the fifth number of the sequence multiplied by $2$ is the sixth number of the sequence.

Example 2

The sequence

$$40,\phantom{\rule{0.33em}{0ex}}35,\phantom{\rule{0.33em}{0ex}}30,\phantom{\rule{0.33em}{0ex}}25,\phantom{\rule{0.33em}{0ex}}20,\dots $$ |

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.

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

$$192,\phantom{\rule{0.33em}{0ex}}96,\phantom{\rule{0.33em}{0ex}}48,\phantom{\rule{0.33em}{0ex}}24,\phantom{\rule{0.33em}{0ex}}12,\phantom{\rule{0.33em}{0ex}}6,\phantom{\rule{0.33em}{0ex}}3,\dots $$ |

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.