Applied Alg2/Trig
11-4: Arithmetic series
Use the sequence 1, 2, 3, 4, …, 97, 98, 99, 100 to answer the
following questions.
1.)
Is it an arithmetic sequence? Why?
2.)
Add the first and last terms of the sequence and write
down the answer. Then add the second and next-to-last
terms. Continue adding terms until you get to the middle
of the sequence. What do you notice in your answers?
3.)
Use your answers to question 2 to find the sum of the
terms of the sequence.
4.)
Describe a short method for finding the following sum.
5  10  15  20  30  35  40  45  50
5.)
What is the sum?
A series is an indicated SUM of the terms of a sequence. Finite
sequences and series have terms that you can count individually
from 1 to a final whole number n. Infinite sequences and series
continue without end. You indicate an infinite sequence or series
with ellipsis points.
FINITE SEQUENCE
FINITE SERIES
6, 9, 12, 15, 18
6 + 9 + 12 + 15 + 18
INFINITE SEQUENCE
3, 7, 11, 15, …
INFINITE SERIES
3 + 7 + 11 + 15 + …
Ex 1 : Use the finite sequence 2, 11, 20, 29, 38, 47. Write the
related series. Then evaluate the series.
SOLUTION: 2 + 11 + 20 + 29 + 38 + 47
The sum of the terms of the sequence is 147.
Ex 2: Write the related series for the finite sequence. Then
find the sum.
100, 125, 150, 175, 200, 225
The first n terms is called a partial sum and is denoted by
Sn .
Arithmetic Series – sum of the terms of an arithmetic sequence.
The sum of the first n terms of an arithmetic sequence can be
represented by the formula
n
Sn   first  last 
2
*** If you know the first term and the nth term of an arithmetic
series you can use the formula.
Ex 1: Find the sum of the first 20 terms of the arithmetic series
5,7,9,11…
Ex 2: Find the sum of the arithmetic series
3 + 8 + 13 + … + 358
Ex 3: Find the sum of the arithmetic series
9 + 20 + 31 + 42 + … + 163
Ex 4: Find the sum of the first 15 terms of the arithmetic series
in which 1st term is 10 and 15thterm is 95 .
Ex 5: Find the sum of the first n terms of the arithmetic series
if n = 20, d = 4 and a1  10 .
Ex 6:
Find the sum of the first n terms of the arithmetic series
1
1
if n = 25 and the arithmetic sequence is 4  4  5  5  ...
2
2
Challenge: Find the sum of the 1st 100 terms of an arithmetic
sequence if the 6th term is 54 and the 10th term is 86.