CPM Homework Help : CC3MN Problem 1-14

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1-14.

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):
Calculate the difference between each consecutive pair of numbers. Do you notice a pattern?
More Help (a):
The sequence is based on addition.
Partial Answer (a):
$1$ , $3$ , $6$ , $10$ , ____, ____
Next: $15$ , $21$

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

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

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

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

Hint (e):
There are two parts to this pattern.
Partial Answer (e):
Subtract $2$ , then add $5$ .

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