CPM Homework Help : AC Problem 1-35

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Home > AC > Chapter 1 > Lesson 1.1.4 > Problem 1-35

1-35.

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

$1$ , $3$ , $6$ , $10$ , ____, ____
Hint (a):
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?
More Help (a):
The sequence is based on addition.
Answer (a):
$1,3,6,10,15,21$

$1$ , $\frac{1}{2}$ , $\frac{1}{4}$ , $\frac{1}{8}$ , ____, ____
Hint (b):
What operation is the sequence based on?
More Help (b):
The sequence is based on division (or multiplication by a fraction).
Answer (b):
$1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \frac { 1 } { 16 } , \frac { 1 } { 32 }$

$1$ , $3$ , $9$ , $27$ , ____, ____
Hint (c):
Look at the last two given numbers of the sequence. What is special about them?
Answer (c):
$1,3,9,27,81,243$

$8$ , $7$ , $5$ , $2$ , ____, ____
Hint (d):
Calculate the differences between each pair of consecutive numbers. What do you notice?
Answer (d):
$8,7,5,2 , - 2 , - 7$

$49$ , $47$ , $52$ , $50$ , $55$ , ____, ____
Hint (e):
There are two parts to this pattern.
Answer (e):
Subtract $2$ , then add $5$ .
$49,47,52,50,55,53,58$

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