untan.ac.id
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
MATHEMATICS FOR ECONOMICS AND BUSINESS
Arithmetic & Geometric Sequence
The students understand the concept of Arithmetic & Geometric Sequence and be able to solve the problems in Economics and Business according to Arithmetic & Geometric Sequence.
untan.ac.id
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Arithmetic
Arithmetic Sequence is a series of numbers in which each pair of numbers differs a fixed (constant) difference. This means if you take any two numbers in an arithmetic row and subtract the first number from the second, the difference will always be the same.
Manual Method:
2, 4, 6, 8, 10 … n
Add the last term with a difference (d)
So, the series above the continued terms are:
10+2 = 12 (a6)
12 + 2 = 14 (a7)
14 + 2 = 16 (a8), etc.
Formula:
an = a1 + (n-1) d
an is nth term
a1 is the 1st term
n is number of terms
d is difference
For example:
2, 4, 6, 8, 10 … n
2 called 1st term (a1)
4 called 2nd term (a2)
n called nth term (an)
Difference (d)
d= an – (an-1)
d= 4-2 = 8-6 = 10-8 = 2
Identify these:
7, 10, 13, 16
5, 10, 15, 20
24, 20, 16, 12
Manual Method:
2, 4, 6, 8, 10 … n
Sum up all of the number series
So, the series above can be:
2+4+6+8+10+…+n
Formula:
Sn = n/2 [2a1 + (n-1)d]
Sn is sum of terms
a1 is the 1st term
n is number of terms
d is difference
untan.ac.id
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Practice…
(1) A student named Budi wants to raise money for summer vacation. He decided to put some money each week into his savings. Initially, he set aside Rp 10,000 in the first week. Every week after, Budi wanted to increase the amount he set aside by Rp 1,000. In other words, he would add $1,000 to the amount he set aside each week. How much should Budi save in the last week of the 4th month?
untan.ac.id
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Practice…
(2) A businessman named Andi owns a shoe store in a small town. He wants to keep track of the profits he earns every month from shoe sales. In the first month, Andi earned a profit of Rp 5,000,000 from selling shoes. Every subsequent month, he hopes to increase his profit by Rp 500,000. If the increase in Andi's store's profit is the same every month, how much will Andi's store's profit be in the 20th month?
untan.ac.id
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Practice…
(3) In a shoe factory, they started the production of new sports shoes. In the first month of production, they managed to produce 100 pairs of shoes. Each subsequent month, they plan to increase production by 20 pairs of shoes. They want to know how many total pairs of shoes they will produce in a year.
untan.ac.id
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Practice…
(4) An entrepreneur named Tono runs a business making creative jewelry from ceramic materials. Every month, Tono's production costs involve raw materials, labor costs, and overhead costs. In the first month, the total production cost was Rp 5,000,000. Tono knows that production costs will increase every month by Rp 500,000. How much does Tono have to spend on a year and a half in total?
untan.ac.id
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Geometric
A geometric Sequence is a row that has a multiplication pattern or has a fixed ratio.
Manual Method:
3, 6, 12, 24, … n
multiple the last term with a ratio (r)
So, the series above the continued terms are:
24 x 2 = 48 (a6)
48 x 2 = 96 (a7)
96 x 2 = 192 (a8), etc.
Formula:
an = a1 . r(n-1)
an is nth term
a1 is the 1st term
n is the number of terms
r is ratio
For example:
3, 6, 12, 24, … n
3 called 1st term (a1)
6 called 2nd term (a2)
n called nth term (an)
Ratio (r)
r = an : (an-1)
d= 6:3 = 12:6 = 24:12 = 2
Identify these:
2, 6, 18 …
4, 12, 36, 108 …
24, 20, 16, 12 …
128, 64, 32, 16 …
Manual Method:
3, 6, 12, 24, … n
Sum up all of the number series
So, the series above can be:
3 +6 + 12 + 24 + … + n
Formula:
Sn = a1(1-rn)/(1-r), or
Sn = a1(rn-1)/(r-1),
Sn is the sum of terms
a1 is the 1st term
n is the number of terms
r is ratio
untan.ac.id
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Practice…
(1) A farmer owns a piece of land used to grow orange trees. Every year, the number of orange trees growing on the land undergoes geometric growth. In the first year, the farmer planted 10 orange trees. He realized that every year, the number of orange trees that grew became three times the number of orange trees in the previous year. That is, this growth ratio is 3, since every year the number becomes tripled. Now, the farmer wants to know how many orange trees will grow on the land in the 5th year?
untan.ac.id
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Practice…
(2) One day, an astronomer named Dina was observing a meteor moving with a certain pattern in the sky. He realized that the meteor was moving with geometric growth. On the first day of observations, Dina noted that the meteor was 10,000 kilometers from Earth. Every day, this meteor gets farther away and its distance from Earth doubles from the previous day. Dina wanted to know how far the meteor was from Earth after 5 days.
untan.ac.id
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Practice…
(3) A farmer has an orchard planted with apple trees. The apple tree bears fruit every year, and each year, the amount of fruit produced by each apple tree increases as the tree ages. In the first year, each apple tree produces 10 apples. Furthermore, every year, the number of apples produced by each apple tree increases by 5 times from the previous year. The farmer wanted to know how many apples his entire apple tree would have been produced in the 5th year.
untan.ac.id
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Play with Balloons…
untan.ac.id
Department of Management
The Faculty of Economics and Business
Universitas Tanjungpura
Strengthening the Ecosystem of Innovation and Collaboration to Realize UNTAN as a Competitive World-Class University
Tutor’s info:
Name: Arman Jaya, S.Pd.I., M.M.
Department: Bachelor’s Degree Program of Management
Phone: 0811220878
Mail: arman.jaya@ekonomi.untan.ac.id
IG: @armandjayalisand