Extended Constructed Response A

Here are some reminders for when you are completing this Extended Constructed Response Task:

• Carefully read each part of the task before writing your response on a sheet of paper.
• Be sure to complete all parts of the task.
• Clearly explain your answer and show all your work.
• Your explanation can include words, tables, diagrams, or pictures.
• You may use a calculator and a ruler for this task.

Carlos wrote the following sequence of numbers on the black board:

2, 6, 18, 54, …

He explained that the rule for his pattern is “Multiply by 3”, since each number is 3 times as much as the number coming before it.

Carlos’s teacher then wrote a new sequence of numbers up on the board:

1, 4, 16, 64, …

Respond to the following questions using the pattern created by Carlos’s teacher.

• What is the rule for the pattern? Explain your reasoning.

• What would the next 2 numbers in the pattern be?

• Will the number 1,100 be part of the pattern? How do you know?