Mathematics 10
SEQUENCES AND SERIES
Sequence - it is an ordered set of numbers formed according to some
pattern or rule
a. 0, 3, 6, 9, 12, …
Series - is a sum of a sequence of terms denoted by “𝑆𝑛 ”
Arithmetic Sequences and
Arithmetic Series
Learning Targets
• I can illustrate arithmetic sequence.
• I can determine arithmetic means, nth term of an arithmetic sequence
and sum of the terms of a given arithmetic sequence.
What is Arithmetic Sequence?
A sequence whose consecutive terms have a common difference is an
arithmetic sequence.
The sequence 𝑎1 , 𝑎2 , 𝑎3 , … 𝑎𝑛 , is arithmetic if there is a number d such that:
𝑎2 − 𝑎1 = 𝑑, 𝑎3 − 𝑎2 = 𝑑, 𝑎4 − 𝑎3 = 𝑑
and so on. The number d is the common difference in the arithmetic
sequence.
Write a formula for the nth term of the given arithmetic sequence.
b. 9, 1, -7, -15, -23, …
Find the 15th term of the arithmetic sequence 18, 22, 26, 30, 34, …
In the arithmetic sequence 8, 14, 20, 26, 32, … , which term is 122?
In the arithmetic sequence 9, 11, 13, 15, 17, … ,
a. write a formula for the nth term,
b. find its 12th term, and
c. which term is 47?
A conference hall has 20 rows of seats. The first row contains 20 seats,
the second row contains 22 seats, the third row contains 24 seats, and
so on. How many seats are there in the last row? How many seats are
there in the conference hall?
A conference hall has 20 rows of seats. The first row contains 20 seats,
the second row contains 22 seats, the third row contains 24 seats, and
so on. How many seats are there in the last row? How many seats are
there in the conference hall?
Determining sum of the
terms of a given arithmetic
sequence.
Find the sum of the first 25 terms of the arithmetic sequence
17, 22, 27, 32, 37, … .
Find the sum of the first 50 terms of the arithmetic sequence if the
first term is 21 and the twentieth term is 154.
Find the sum of the first 25 terms of the arithmetic sequence
17, 22, 27, 32, 37, … .
Find the sum of the first 50 terms of the arithmetic sequence if the
first term is 21 and the twentieth term is 154.
Find the sum of the first 10 terms: 𝑎1 = 103 and 𝑑 = 3
Determining arithmetic means
Insert four arithmetic means between 15 and 45.
Insert three arithmetic means between 11 and 35.
Insert four arithmetic means between 15 and 45.
Insert four arithmetic means between 15 and 45.
Insert three arithmetic means between 11 and 35.
Insert three arithmetic means between 11 and 35.