Warm UP!. Identify the following as Arithmetic, Geometric, or neither: 2, 7, 12, 17, … 2. Find the nth term for the sequence: 2, 20, 200, 2000, … 3. Generate the first four terms of the sequence given its recursive formula: a 1 = 6 and a n = 2a n-1 + 3
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Identify the following as Arithmetic, Geometric, or neither: 2, 7, 12, 17, …
2. Find the nth term for the sequence: 2, 20, 200, 2000, …
3. Generate the first four terms of the sequence given its recursive formula: a1 = 6 and an = 2an-1 + 3
4. Find the 150th term of the sequence an = 0.5n + 8
Graphical interpretation of limits for explicit sequences investigationComplete the task. You may work with a partner. You have 20 minutes.
LG 6-2: Limits of Sequences
The sequence converges to a unique value: 0
We write this as
The sequence converges to a unique value: 1
We write this as
This sequence diverges. You can see it is going up – to infinity.
We can write this as
Given a sequence an there are several possibilities as to its convergence behavior:
When a geometric sequence is in explicit form, you only need to use the common ratio to determine the limit as the sequence approaches infinity.
The geometric sequence a1(r)n-1 is divergent if |r| > 1 or r > 1 and converges to 0 if |r| < 1.
5. 8, -5, 8, -5, 8,. . .
Estimate the limits: