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9.2
Arithmetic Sequences and Partial Sums
Homework for section 9.2
p657
#7-13, 19, 21, 25-29, 35, 37,
47-73, 83-87, 93, 95.
Arithmetic Sequence:
a 1, a 2 , a 3 , a 4 ...
a sequence whose consecutive
terms have a common difference.
is an arithmetic sequence I F
a2  a1  a3  a2  a4  a3  d
a1  d  a2
a1  d  d  a3
a1  2 d  a3
a1  d  d  d  a4
a1  3 d  a4
a1  d  d  d  d  a5
a 1  4d  a 5
Figure out the formula for the nth term…
7, 11, 15 , 19 ......
n
1
2
3
4
n th term
7
11
15
19
d=?
a n  4n  3
Figure out the formula for the nth term…
2 , 3 , 8 , 13 ......
n
1
2
3
4
n th term
2
3
8
13
d=?
a n  5 n  7
an  7  5 n
Figure out the formula for the nth term…
5 3 7
1,
,
, , ......
4 2 4
n
n th term
1
2
3
4
1
5
4
3
2
7
4
d=?
an
an
n 3

4
n
3


4
4
Arithmetic Sequences have the form:
where d  common difference
a n  dn  c
and
c  a1  d
Find the formula for the nth term of an arithmetic
sequence where d = 3, and a1 = 2
an = 3n-1
Try this:
The 4th term of an arithmetic sequence is
20, the 13th term is 65. What are the first
8 terms of the sequence?
5, 10, 15, 20, 25, 30, 35, 40
Try this:
Find the 9th term of an arithmetic sequence
that begins with 2 and 9.
58
Sum of a Finite Arithmetic Series…
Sn
n

a 1  a n 
2
w here n is the number of terms
a 1 is the f irst term
a n is the last term
Add up the first 10 odd numbers……
Sn 
10
2
1  19 
 10 0
Find the 150th partial sum of:
5, 16, 27, 38, 49……
123675
An object with negligible air resistance falls out of a extraterrestrial
spaceship buzzing the locals somewhere in the heart of Texas... If
the object falls 4.9 meters in the first second, 14.7 meters in the
second second, 24.5 meters in the third second, and so on, how
far will the object fall in the 6th second? In 6 seconds?
An auditorium has 20 rows of seats. There are 20
seats in the first row, 21 in the second, 22 in the third,
and so on. How many seats are there in total?
590
Go!
Do!