PreCalc 12/11
Unit 1 Sequences & Series
Day 2 Notes
Arithmetic Series
Sometimes it is more useful to keep track of not only each term in a sequence but the
TOTAL (sum) of those terms as we go.
Discuss a situation when you might want to keep track of a sum (series) instead of each
term (sequence).
As before, we have some useful formulas we can use when looking at an arithmetic
series. To find the sum of a series (Sn)
Sn 
Ex 1
(a  tn )
xn
2
Determine the sum of:
a) 2 + 6 + 10 + 14
b) 2 + 6 + 10 +…. + 150
c) The first 20 terms of an arithmetic series with a = 6 and d = 2/3
d) 2 +
9
+ ….. + 142
2
PreCalc 12/11
Unit 1 Sequences & Series
Day 2 Notes Page 2
Sigma Notation
We have noticed that with the series we sometimes have to list many numbers in a row.
There is a way to express all these numbers in an abbreviated form.
2 + 4 + 6 + 8 + 10
could be expressed as
2(1) + 2(2) + 2(3) + 2(4) + 2(5)
we write this as
5
Ex 1
Simplify
 3n  1
n 2
7
Ex 2
Simplify
h 3
Matty 2014
3
2h2
PreCalc 12/11
Unit 1 Sequences & Series
Day 2 Notes Page 3
TI83 Users:
You MUSH ALWAYS show your work when doing these this unit, but you can use your
TI83 to double check answers.
Here’s How:
You will need:
sum( -> found under 2nd stat -> Math -> #4: sum(
seq( -> found under 2nd stat -> Ops -> #5: seq(
So lets try on the second page examples:
sum(seq(2x,x,1,5,1)
The 2x is referring to the 2n, the x is our variable (our calculator uses x for all variables,
1 is your starting point, 5 is your ending point, the last 1 must be inserted for the program
to work (because for sigma notion using sum and seq, we need a domain greater than
1…) just put it in at the end 
Try it yourself:
Matty 2014