9.2 Arithmetic Sequences and Partial Sums

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9.2 Arithmetic Sequences and Partial Sums
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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 3 or 2, -3,
-8, -13, , 7 - 5n are arith. seq.s
Lets take a look at the first example. What is
d, the common difference? What is a1?
a1 7
a4 7 3(4) 19
a2 7 4 11
Do you see a pattern? What is a5?
What is an?
a3 7 2(4) 15
What is the 35th term?
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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 a1 5 and a1 7
How now, do we find the 18th term?
a18 a1 17d 7 17(5) 92
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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
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The fourth term of an arithmetic sequence is 20,
and the 13th is 65. 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
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The sum of a finite arithmetic sequence
Ex. Add the numbers from 1 to 100.
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It would take way too long to do this by hand.
Using the formula just given, we can do it in
seconds.
Find the sum.
First, we have to find a1 and a150.
a1 a150
Now substitute those into the formula.
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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?
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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 20 19(1) 39 seats in the last row.
Now find S.
590
Homework 39-79 odd