Sequences
Definition of arithmetic sequence.
a sequence of numbers such that difference between the consecutive terms is constant (via Adding or subtracting).
13, 10, 7, 4, ____,
1
The sequence in which common difference is used.
arithmetic sequences.
d =
the common difference.
What is this formula used for
tn+1 = tn + d
the explicit formula for arithmetic sequences.
Definition of geometric sequences.
A sequence of numbers such that the terms have a common ratio between them.
8, 8.5, 9, 9.5, 10, ____, ____, ...
What is 10.5 and 11.
The sequence in which common ratio is used.
geometric sequences.
r =
the common ratio.
What is this formular used for
tn+1=r*tn
Geometric sequences
The variable d.
the common differences used for arithmetic sequences.
t4 = _____ if a sequence has a formula of tn+1 = tn +5 and t1 = 7
27.
Construct a recurrence relation for the following sequence 11, 15, 19, 23, 27,...
t0=2, tn+1=tn + 4
tn =
the nth term.
Write the 5th term in the sequence defined by the recurrence relation:
A0=132, An+1=An-17
64
The variable r.
the common ratio used for geometric sequences.
t7 for the following sequence:
81, 27, 9, 3,...
t6 = 1/9
Construct a recurrence relation for the following sequence 2, 8, 32, 128, 512,...
t0=2, tn+1=4*tn
t0 =
the initial term of the sequence.
The number of students at a school increases by 125 a year. In the first year, there are 300 students. Construct a recurrence relation for the scenario
t0=300, tn+1=tn+125
Explain a real world application for both arithmetic and geometric sequences.
Answers vary but need an arithmetic and geometric real world application: At teacher discretion.
t4 of the following sequence:
-5, 15, -45,...
t4 = -405
1, 1/2, 1/4, 1/8, 1/16...
t0=1, tn+1=1/2*tn
tn-1 =
the previous term than the nth term.
A swarm of bees increases geometrically. The swarm has 150 bees in the first week, and 600 bees in the second week.
construct a recurrence relation for the population of bees
t0=150, tn+1=4* tn