Name: ________________________
Date: _________ Block: 1 4 7
Mrs. Mistron
Warm Up Fill out the table for the following functions:
1.
2.
y  2 x2  1
x
2
1
0
1
x
y   x3
1
2
3
4
A sequence is a function whose domain is a set of
consecutive integers which start at one (unless otherwise
stated). The values in the range of the function are called
the terms of the sequence.
Domain: 1
2
3
4
…
n
Range: a1
a2
a3
a4
… an
(relative position of each term)
(terms of the sequence)
A sequence can be expressed by an equation, or a rule. The rule can
either be explicit (like an  2n ) or recursive (like an  an  1  2; a1  2 )
EXAMPLE ONE Write the five terms of the explicit sequences.
(A) an  2n  5
(B) f (n)   3
n 1
EXAMPLE TWO Write the explicit rule for the following sequences.
(A) 1,  4,  9, 16,  25, ...
(B) 0, 2, 6, 12, 20, ...
Series and Summation Notation
A series is the expression that arises from adding the terms of a sequence
together. To write a series, summation notation can be used.
2468 
4
 2i
i 1
EXAMPLE THREE Write the series in summation notation, then find the sum.
(A) 5  6  7  ...  12
(B) 5  10  15  20
Recursive Sequences
Another way to define a sequence is with a recursive rule. In a recursive
rule, the first term(s) is given along with a recursive equation that states
how an is related to a previous term(s).
EXAMPLE FOUR List out the first five terms in the recursive sequence
(A) a0  1; an  an  1  4
(B) a1  2; an  3  an  1
EXAMPLE FIVE Write the recursive rule for the following sequences
(A) 3, 13, 23, 33, 43, ...
(B) 16, 40, 100, 250, 625, ...
(C) 1, 1, 2, 3, 5, 8, 13, ...
(D) 1, 1, 2, 6, 24, 120, ...
EXAMPLE SIX An online music service initially has 50,000 members. Each
month, it loses 20% of its current membership, then adds 5,000 new members.
(A)Write a recursive rule for the number of members, an , at the start of the
nth year.
(B) Use your calculator to find the number of members at the start of the
fifth year.
(C) What happens to the number of members each year?
Homework Explicit vs. Recursive Sequences Worksheet