# arithmetic sequences ```Notes 6-5
Pre-Calculus
Section 9.1 &amp; 9.2
Properties of Sums
1.
2.
3.
4.
1. Use the properties of sums to help you find the sum.
a.
4
 12
b.
6
 5(2)i
i1
c.
3
 (4i  2i )
d.
i 1
i1
2
 (2i  3 )
i
i 1
SERIES
Consider the infinite sequence: a1, a2, a3, …
1. The sum of the first n terms of the sequence is called a _______________________ or the
_______________________ of the sequence.
It is denoted by:
2. The sum of all of the terms of the infinite sequence is called an _________________
It is denoted by:
For the series

3
 10
i 1
i
find (a) the third partial sum and (b) the sum
(a)
Using sigma notation, write the following sum:
(b)
1
1
1
+ 3(2) + 3(3) +
3(1)
1
⋯ + 3(9)
Definition:
ARITHMETIC SEQUENCES
Formula:
Decide if the following sequences are arithmetic. If so, find the COMMON DIFFERENCE.
7, 11, 15, 19…
2, -3, -8, -13
log2 1, log24, log216, log264….
1, 4, 9, 16….
log 10, log 11, log 12, log 13,……
Find a formula for the nth term of the following arithmetic sequences. Then find the indicated term.
a1 =2 , common difference = 3; a23=?
common difference = -9, a1= 13; a10=?
Find a formula for the nth term for the sequence given that a1 = 3 and a3 = 9.
Find a formula for the nth term for the sequence given that a7 = -19 and a10 = -28.
Find a formula for the nth term of the arithmetic sequence that begins… 2, 9, ….. Then find a9.
If the sixth term of an arithmetic sequence is 20.6 and ninth term is 30.2, then what is the twentieth
term?
The Sum of a Finite Arithmetic Sequence:
8
Find the indicated partial sum:  3n  6
i 1
400
Find the partial sum  2n  3
n 1
Find the sum of the integers from 1 to 100.
Find the 150th partial sum of the
sequence: 5, 16, 27, 38, 49, …..
Find the arithmetic sequence that would produce the following values.
Then find the position “n” of the last given term.
25, 33, 41, …,145
Use sigma notation to write the sum: 12 + 18 + 24 … +5
40, 37, 34, …,-29
```