1. 9.2 Arithmetic Sequences and Partial Sums

2. 9.2 Arithmetic Sequences
A sequence is arithmetic if the differences between
consecutive terms are the same.
That common difference is called d.
For Ex. 7, 11, 15, 19, … , 4n or
2, -3, -8, -13, … , 7 - 5n are arith. seq.’s
Let’s take a look at the first example. What is d, the
common difference? What is a1?
a1 = 7
a4 = 7 + 3(4) = 19
a2 = = 11
Do you see a pattern?
What is a5?
What is an?
a3 = 7 + 2(4) = 15
What is the 35th term?

3. Can you come up with an equation that will give you the nth
term of any arithmetic sequence?
an = a1 + (n - 1)d
Find a formula for the nth term of the arithmetic sequence
whose common difference is 5 and whose 2nd term is 12.
What is the 18th term of the sequence?
What do we know?
That d = 5 and a2 = 12
a2 = a1 + (2-1)d or a1 + d
Substitute in for a2 and d
and solve for a1
12 = a and a1 = 7
How now, do we find the 18th term?
a18 = a1 + 17d = (5) = 92

4. Find the ninth term of the arithmetic sequence whose
first two terms are 2 and 9.
What is the common difference, d?
d = 7
Now we can find the 9th term because we know a1 and d.
Find a9.
a9 = 2 + 8(7) = 58

5. The fourth term of an arithmetic sequence is 20, and the
13th is Write the first 4 terms of this sequence.
Write the equations of any 4th and 13th terms of any
arithmetic sequence.
a4 = a1 + 3d
a13 = a1 + 12d
Now fill in what we know and
use ellimination to find a1 and d.
So the first four terms are:
5, 10, 15, 20
Homework 1-37 odd

6. The sum of a finite arithmetic sequence
Ex. Add the numbers from 1 to 100.

7. Find the sum.
It would take way too long
to do this by hand. Using
the formula just given, we
can do it in seconds.
First, we have to find a1 and a150.
a1 =
a150 =
Now substitute those
into the formula.

8. Insert 3 arithmetic means between 4 and 15.
4 ____ ____ ____ 15
We need to find the common difference.
Write the equation for a5.
a5 = a1+ 4d
15 = 4 + 4d
So the sequence is?

9. An auditorium has 20 rows of seats. There
are 20 seats in the first row, 21 in the the
second row, 22 in the third row, and so on.
How many seats are there in all 20 rows?
So, what do we know? Do we know a1? d?
Do we know how many seats are in the last
row? a20
a20 = (1) = 39 seats in the last row.
Now find S.
= 590
Homework odd