Series
Notes #____
IB Math Studies I
Arithmetic Series
Series:
Gauss Story: What is the sum of the integers from 1 to 100?
Arithmetic Series Formulae
Examples:
1. Find the sum of 8 + 11 + 14 + 17 + 20 +23
a) By simple addition
b) Using the first formula
c) Using the second formula
2. Find the sum of 100 + 93 + 86 + 79 + … to 40 terms.
3. An arithmetic series has 11 terms. The first term is 6 and the last term is -27. Find the sum
of the series.
4. A bricklayer builds a triangular wall with layers of bricks as shown. If the bricklayer uses 171
bricks, how many layers did he build?
5. Three consecutive terms of an arithmetic sequence have a sum of 12 and a product of -80.
Find the terms.
Series
Notes #____
IB Math Studies I
Geometric Series
Geometric Series Formulae
Examples:
1. The following numbers form a geometric sequence: 3, 12, 48, …
a) Write down the common ratio.
b) Find the value of the 10th term.
c) Find the sum of the first 10 terms.
2. The following numbers form a geometric sequence: 20, 10, 5, …
a) Write down the common ratio.
b) Find the value of the 10th term.
c) Find the sum of the first 10 terms.
3. Amelia got a new job with a starting an annual salary of $21,000 per year with an annual raise
of 4% of the previous year’s salary.
a) Write down the common ratio.
b) Determine the Amelia’s salary during the second year.
c) In which year will her salary first exceed $25000?
d) Amelia decides to quit her job after 10 years. How much total money has she made
with the company?