MCR3U1
U7L1
DISCRETE FUNCTIONS ~ SEQUENCES AND SERIES
(Arithmetic Sequences)
PART A ~ INTRODUCTION
A numerical sequence is a set of numbers arranged in an order.
A sequence may have a finite or an infinite number of terms.
Ex. 1, 4, 9, 16, 25, 36, 49, …
The notation used to represent the terms of a sequence is:
𝑡1 → the 1𝑠𝑡 term
𝑡2 → the 2𝑛𝑑 term
𝑡𝑛 → the 𝑛𝑡ℎ term
Sometimes a pattern can lead to a general rule for determining the terms of a sequence.
This rule is called the formula for the 𝒏𝒕𝒉 term or the general term (𝒕𝒏 ).
Ex. 𝑡𝑛 = 𝑛2
PART B ~ ARITHMETIC SEQUENCES
arithmetic sequence:
a sequence where the difference between consecutive
terms is a constant
common difference (𝒅):
the amount that is added (or subtracted) to each term
of a sequence to get the next term of the sequence
Ex.
1, 5, 9, 13, …
or
1, –3, –7, –11, …
DERIVING THE GENERAL TERM (𝒕𝒏 )
𝑡1 ,
𝑡2 ,
𝑡3 ,
𝑡4 ,
𝑡5 , … 𝑡𝑛
GENERAL TERM of an ARITHMETIC SEQUENCE
𝑡𝑛 = 𝑎 + (𝑛 − 1)𝑑
where 𝑎 is 𝑡1 (the first term)
𝑛 is the number of terms
𝑑 is the common difference
( 𝑑 = 𝑡𝑛 − 𝑡𝑛−1 )
MCR3U1
U7L1
PART C ~ EXAMPLES
Ex 
Determine which of the following are arithmetic sequences. If they are, state
the common difference (𝑑).
a)
2, 7, 12, 17, …
b)
6, 10, 12, 13, …
c)
5, 2, –1, –4, …
Ex 
Given 𝑡1 = 7 and 𝑑 = 3 for an arithmetic sequence, write the first four terms of
the sequence and state the general term (𝑡𝑛 ).
Ex 
State the general term and then calculate 𝑡15 for the given arithmetic sequence:
3, 7, 11, 15, …
Ex 
Calculate the number of terms in the given arithmetic sequence:
9, 4, –1, …, –146
MCR3U1
U7L1
Ex 
The third term of an arithmetic sequence is –11 and the seventh term is –27.
Determine the first three terms of the sequence.
Ex 
Boxes are stacked in a store display in the shape of a triangle. The number of
boxes in the rows form an arithmetic sequence. There are 41 boxes in the third
row from the bottom and 23 boxes in the twelfth row from the bottom.
a)
b)
Ex 
Determine the values of 𝑎 and 𝑑 for this sequence.
Determine the maximum possible number of rows of boxes.
Determine the value of 𝑥 that makes the given sequence arithmetic:
2𝑥 + 9, −4𝑥, −3𝑥 + 5, …
HOMEWORK: p.424–425 #1, 3, 4, 8(parts i & iii), 10, 13ace, 15