### Home > ACC7 > Chapter cc31 > Lesson cc31.1.2 > Problem1-14

1-14.

Copy and complete each sequence below. Using words, not numbers, describe how the patterns work. (For example, write, “Double the previous number.”) Homework Help ✎

1. $1$, $3$, $6$, $10$, ____, ____

• Calculate the difference between each consecutive pair of numbers. Do you notice a pattern?

The sequence is based on addition.

$1,\ 3,\ 6,\ 10,\ \text{__, __}$

Next: $15$, $21$

1. $1$, $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{8}$, ____, ____

• What operation is the sequence based on?

The sequence is based on division (or multiplication by a fraction).

$\frac { 1 } { 2 } ,\ \frac { 1 } { 4 } ,\ \frac { 1 } { 8 } ,\ \text{__, __}$

$\text{Next}: \frac{1}{16}, \frac{1}{32}$

1. $1$, $3$, $9$, $27$, ____, ____

• Look at the last two given numbers of the sequence. What is special about them?

$1,\ 3,\ 9,\ 27\ \text{__, __}$

Next: $81$, $243$

1. $8$, $7$, $5$, $2$, ____, ____

• Calculate the differences between each pair of consecutive numbers. What do you notice?

$8,\ 7,\ 5,\ 2,\ \text{__, __}$

Next: $−2$, $−7$

1. $49$, $47$, $52$, $50$, $55$, ____, ____

• There are two parts to this pattern.

Subtract $2$, then add $5$.