Arithmetic Sequence and Arithmetic Series

ARITHMETIC In this lesson you will learn to
• Illustrate an arithmetic sequence
SEQUENCE AND • Determine the nth term of an

arithmetic sequence
ARITHMETIC SERIES
• Find the arithmetic means and
sum of the terms.
ARITHMETIC SEQUENCE
A sequence whose consecutive terms have a common difference is
an arithmetic sequence.
The sequence is arithmetic if there is a number d such that:
and so on. The number d is the common difference in the

arithmetic sequence.
FORMULA FOR THE NTH TERM
OF AN ARITHMETIC
SEQUENCE
The nth term, of an arithmetic sequence with
first term, and common difference, d, is given
by
EXAMPLE 1
Write a formula for the nth term of the given arithmetic sequence.
A) 11, 18, 25, 32, 39, …
Solution:
Each term is 7 more than the previous terms, so d = 7, .
Check: Substitute a few

terms
B) 9, 1, -7, -15, -23, …
Given:
Solution:

terms
C) 5, 7, 9, 11, 13, …
Given:
Solution:

terms
LET’S TRY THIS!
Write the formula for the nth term of the given arithmetic sequence.
A) -2, 1, 4, 7, 10,…
Given:
Solution: Check: Substitute a few

terms
FINDING THE TERM WHEN
PLACE OF TERM IS GIVEN
Example:
1) Find the 15th term of the arithmetic sequence 16, 20 ,24, 28, 32, …
Solution:
Note that
2) Find the 12th term of the arithmetic sequence 9, 12, 15, …
Given:
Solution:
3) Find the 9th term of the arithmetic sequence 1, , , …
Given:
Solution:
4) Find the 8th term of the arithmetic sequence , …
Given:
Solution:
5) Find the 13th term of the arithmetic sequence 7, 15, 23, 31, 39, …
Given:
Solution:
DETERMINING THE PLACE OF
TERM.
Example:
1) In the arithmetic sequence 6,12, 18, 24, 30,…, which term is 84?
Solution:
Find n when
Therefore, 84 is the 14th term of the sequence.

2) In the arithmetic sequence 7, 13, 19, 25, 31, …, which term is 67?
Find n when

Find n when

Find n when

5) In the arithmetic sequence 3, 9, 15, 21. …, which term is 63?
Find n when

SOLVING COMMON
DIFFERENCE
Example:
1) Find the 18th term of the arithmetic sequence whose first term is 11 and whose
seventh term is 59.
Solution:
Find the common difference, d, by substituting and into formula
Given:
2) Find the 15th term of the arithmetic sequence whose first term is 9 and whose fifth term is 33.
Solution:
Given:
thirteenth term is 40.
Solution:
Given:
twelfth term is 58.
Solution:
Given:
fourteenth term is 96.
Solution:
Given:
Go to Assessment and answer the activity.
PROBLEM
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?
SOLUTION
Sequnce: 20, 22, 24, … , Sequence: 20, 22, 24, 26, 28, 30, 32,
34, 36, 38, 40, 42, 44, 46, 48, 50, 52,
Given:
54, 56, 58.
= 780
Thus, there are 58 seats in the last row.

SUM OF THE FIRST N TERMS
OF AN ARITHMETIC
SEQUENCE
Given an arithmetic sequence where
is the first term and , is the nth term,
the sum of the first n terms is given
by:
Sequence: 20, 22, 24, … , Given:
Given:
Thus, there are 780 seats in the

Thus, there are 58 seats in the last row. conference hall.
EXAMPLES:
Find the sum of the first
A. 25 terms of the arithmetic sequence 18, 23, 28, 33, 38, …,
B. 50 terms of the arithmetic sequence if the first term is 21 and the twentieth term
is 154.
C. 18 terms of the arithmetic sequence whose general term is
A. 18, 23, 28, 33, 38, …,
Find the 25th or the last term of a sequence.
Given: Given:
B. 50 terms of the arithmetic sequence if the first term is 21 and the twentieth term
is 154.
Find the common difference.
Find
Given:
C. 18 terms of the arithmetic sequence whose general term is
Find the first term and last term.
1) A pyramid of empty cans has 30 blocks in the bottom
row and one fewer can in each successive row thereafter.
How many cans are there in the pyramid?
2) Find the seating capacity of a movie house with 40

rows of seats if there are 25 seats in the first row 28 seats
in the second row, 31 in the third row and so on.

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ARITHMETIC In this lesson you will learn to

• Illustrate an arithmetic sequence

SEQUENCE AND • Determine the nth term of an

and so on. The number d is the common difference in the

Check: Substitute a few

Check: Substitute a few

Check: Substitute a few

Solution: Check: Substitute a few

Therefore, 84 is the 14th term of the sequence.

Therefore, 67 is the 11th term of the sequence.

Therefore, 44 is the 12th term of the sequence.

Therefore, 63 is the 15th term of the sequence.

Therefore, 63 is the 15th term of the sequence.

A conference hall has 20 rows of seats.

Thus, there are 58 seats in the last row.

Thus, there are 780 seats in the

2) Find the seating capacity of a movie house with 40

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