1. Core Connections, Algebra 1 Name: __________________________
Team Assessment Date:_______________Per:_________
Each team member is responsible for his or her own paper. Show all of your work clearly and completely.
1. Jonnique and Emma were discussing two sequences. Jonnique was writing out the first ten
terms of the sequence given by t(n) = 6n - 6 and Emma was writing down the first ten terms of
the sequence t(n) = 3n + 60 , when the teacher asked them whether their two sequences had
any terms in common.
“Well, none of the first ten terms are the same,” Emma said.
“But that doesn’t mean there isn’t a term in common later in the sequence,” Jonnique
responded. “How can we check?”
“I know,” Emma said quickly. “If the graphs of the sequences cross, then they must have a
term in common. The graphs of these sequences are linear, and since they aren’t parallel, they
must cross! We’re done!”
“Wait a minute!” Jonnique exclaimed. “If both sequences have positive slopes but one starts
with a negative and the other a positive, they will never have a term that is the same!”
Help Jonnique and Emma by discussing Emma’s conclusions to see if Emma or Jonnique is
correct. Then, find any terms the two sequences have in common if Emma is correct. If
Jonnique is correct in saying that they don’t share a term, please explain why not.

2. 2. Margot was doing her homework when her dog bit off the last part of the paper. All she had left
was the first part of the sequence: 4, 12, ... and the fact that 972 was some term of the sequence.
a. Could the sequence be arithmetic? If so, what is the equation of the nth term and what term
number is 972? If no, explain why not.
b. Could the sequence be geometric? If so, make a table to show what term number is 972. If
no, explain why not.

3. 1. The two sequences do share a term. The 22th
term in each sequence is 126. Emma is correct.
2. a: yes, , ; b: yes, ,