Download 1 Recursive sequences: Examples: Example Find the first 4 terms

9.4 Sequences
Name: __________________
Objectives: Students will be able to express arithmetic and
geometric sequences explicitly and recursively; they will also be able
to find limits of convergent sequences.
Sequences:
Examples:
Finite
Infinite
Example Find the first 6 terms and the 100th term of the sequence
defined by ak = k2 - 1.
Mar 19­5:14 PM
Recursive sequences:
Examples:
Example Find the first 4 terms and the 8th term of the
recursively defined sequence.
c1 = -2, c2 = 3 and ck = ck-2 + ck-1, for k ≥ 3.
Mar 19­5:18 PM
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Limit of a Sequence Let {an} be a sequence of real numbers, and
consider lim an . If the limit is a finite number L, the sequence
n --> ∞
__________ and L is the _____ ___ _____ ____________.
If the limit is infinite or nonexistent, the sequence _________.
Examples Determine whether the sequence converges or diverges.
If it converges, find the limit.
1.) 1, 1/2, 1/3, 1/4, ..., 1/n, ...
2.) 2, 3/2, 4/3, 5/4, ...
3.) 2, 4, 6, 8, 10, ...
Mar 19­5:25 PM
4.) -1, 1, -1, 1, -1, 1, ...
5.)
3n
n +1
6.)
5n2
n3 + 1
7.)
n3 + 2
n2 + n
Mar 19­5:29 PM
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Arithmetic Sequences
Example:
Common difference:
Defined recursively:
Defined explicity:
Example Find the common difference, the 10th term, a recursive
rule and an explicit rule.
-6, -2, 2, 6, 10, ...
Mar 19­5:32 PM
Geometric Sequences
Example:
Common ratio:
Defined recursively:
Defined explicity:
Example Find the common ratio, 10th term, a recursive rule and an
explicit rule.
3, 6, 12, 24, 48, ...
Mar 19­5:36 PM
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Examples
1.) The fifth and ninth terms of an arithmetic sequence are -5 and
-17, respectively. Find the first term and a recursive rule for the
nth term.
2.) The third and sixth terms of a geometric sequence are -75 and
-9375, respectively. Find the first term, common ratio and an
explicit rule for the nth term.
Mar 19­5:37 PM
Example Graph the sequence bn = √n - 3.
Example Pat designs a patio with a trapezoid-shaped deck
consisting of 16 rows of congruent slate tiles. The number of tiles
in the rows forms an arithmetic sequence. The first row contains
15 tiles and the last row contains 30 tiles. How many tiles are used
in the deck?
Assignment: Pages 749-750 # 1-39 odd, 43-48
Mar 19­5:39 PM
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