Aim #89: How do we find the sum of the terms of an arithmetic sequence?
Homework: Handout
Do Now: 1) Find the number of terms in the following sequence:
-8, -2, 4, 10, . . . 52.
2) The following diagram forms a sequence based upon the number of toothpicks
needed to create the shapes:
a) Write a numerical sequence to represent this sequence.
b) Assuming the pattern continues, write an explicit formula that determines an,
the number of toothpicks in the nth term. How many toothpicks are needed to
create the 15th term?
What is a series?
A series is the sum of terms of a sequence.
We denote sum with greek symbol "sigma" Ʃ
-Determine the sum of the first positive 100 integers.
-Let's write the sequence from do now question #1 in sigma notation:
1) Given the sequence:
20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70
a) Write the equation for the arithmetic sequence:
b) Express the sum of the sequence in sigma notation.
c) Find the sum of the sequence.
To find the sum of an arithmetic sequence (called an arithmetic series) we can
use the following formula:
n(a 1 + a n )
Sn =
2
# of terms of sequence being added
d) If our sequence were to continue, find the sum of the first 30 terms of this
sequence.
2) Write the series in sigma notation:
3 + 5 + 7 + 9 + 11 + 13 + 15
3) Find the sum if you are given the following information: a1 = 24, an = 0, d = -6
4
4) Write the sum given by Σ (k + 5).
k=1
4
5) Write the sum given by Σ k + 5
k=1
6) Find the value of the following summation:
7) Given the sequence: 3, 6, 9, 12, 15, 18, 21
a) Find the formula for this sequence.
b) Express the sum of this sequence in sigma notation.
c) Find the sum of the sequence.
8) In a theater, there are 20 seats in the first row. Each row has 3 more seats
than the row ahead of it. There are 35 rows in the theater. Find the total number
of seats in the theater.
9) In a certain arithmetic sequence a4 = 10 and a8 = 54, find a26 and find the sum
of the first 10 terms.
Sum It Up!
A series is the sum of a sequence. We use sigma notation to write it concisely.
Upper Bound
4
Σ (k + 5).
k=1
Lower Bound
Formula