Patterns and Sequences in Mathematics

What is the missing term and the rule in the pattern: 65.9, 65.3, ____, 64.1, 63.5, 62.9?

• 64.7; Rule: Subtract 0.6 each time

• 64.5; Rule: Subtract 0.8 each time

• 64.3; Rule: Subtract 0.7 each time

• 64.9; Rule: Subtract 0.5 each time

A state park rents canoes to use on the river. It costs $5.00 to rent a canoe for 1 hour, $6.75 for 2 hours, $8.50 for 3 hours, and $10.25 for 4 hours. If this pattern continues, how much will it cost to rent a canoe for 7 hours?

• $15.75

• $15.50

• $12.00

• $20.00

Look at the number pattern: 8.70, 8.45, 8.20, 7.95, ... Which number comes next in the pattern?

• 7.70

• 7.50

• 7.45

• 7.25

What is the rule for the pattern: 1/8, 3/8, 5/8, 7/8?

• Add 1/8 each time

• Add 2/8 each time

• Subtract 1/8 each time

• Subtract 2/8 each time

Based on the rule, what would be the next two numbers in the pattern: 1/8, 3/8, 5/8, 7/8?

• 9/8, 11/8

• 8/8, 9/8

• 7/8, 8/8

• 10/8, 12/8

A cupcake bakery always purchases extra sugar. The input represents how much sugar was purchased, and the output represents how much sugar is needed. If a bakery purchased 5 4/5 pounds of sugar, how much sugar was needed according to the rule?

• 4 2/5 pounds

• 4 1/5 pounds

• 2 1/5 pounds

• 5 1/5 pounds

Answer explanation

1. Understand the Rule: The rule is to subtract 7557​ pounds from the purchased amount to determine the actual amount of sugar needed.

2. Convert the Mixed Number to an Improper Fraction: To make calculations easier, convert the mixed number 545554​ to an improper fraction.

   545=5×5+45=25+45=295554​=55×5+4​=525+4​=529​

3. Apply the Rule: Subtract 7557​ from 295529​:

   295−75=29−75=225529​−57​=529−7​=522​

4. Convert the Improper Fraction Back to a Mixed Number: Convert 225522​ back to a mixed number:

   225=425522​=452​

Conclusion:

If the bakery purchased 545554​ pounds of sugar, they needed 425452​ pounds of sugar according to the rule.

Summary:

• Purchased Amount: 545554​ pounds

• Rule: Subtract 7557​ pounds

• Needed Amount: 425452​ pounds

• 4

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