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Tell students that the sequences they have seen today (in this activity and in the warm-up) have a special name: geometric sequences. Geometric sequences are characterized by a common ratio. In a geometric sequence if you divide any term by the previous term, you always get the same value: the common ratio for the sequence. Reiterate that the common ratio for the area sequence is
because it’s what you multiply by to get the next term. 2.3 Complete the Sequence
10 minutes
The purpose of this task is to solidify what it means for a sequence to be geometric and to practice working with the idea of a common ratio.
Student Task Statement
1. Complete each geometric sequence.
a. 1.5, 3, 6, ___, 24, ___
b. 40, 120, 360, ___, ___
c. 200, 20, 2, ___, 0.02, ___
d. , ___, , , ___
e. 24, 12, 6, ___, ___
2. For each sequence, nd its common ratio.
Student Response
1. First question: a. 12, 48
b. 1080, 3240 c. 0.2, 0.002
d. ,
e. 3, 1.5
2. Second question:
a. 2
b. 3
c.
d. 3 e.
Unit 1
Lesson 2: Introducing Geometric Sequences 23