### Home > AC > Chapter 1 > Lesson 1.1.4 > Problem1-35

1-35.

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

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

What is the difference between consecutive numbers in the sequence? How does the difference between two numbers compare with the difference between two different numbers?

The sequence is based on addition.

$1,3,6,10,15,21$

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).

$1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 16 } , \frac { 1 } { 32 }$

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

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

$1,3,9,27,81,243$

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

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

$8,7,5,2 , - 2 , - 7$

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

There are two parts to this pattern.

Subtract $2$, then add $5$.

$49,47,52,50,55,53,58$