Geometric Sequence Formulas and Example Problems

Formula.co.id – After previously we discussed about volume formula this time we will discuss material about geometric formulas, we will describe in detail and complete the understanding of geometric series, elements, formulas, and examples of problems from geometry.

Definition of Geometry

What is Geometry? you already know, Geometry is a branch of mathematics concerned with studying the relationship between points, lines – lines, planes, shapes, sizes, relative positions of images, the nature of space, as well as planes and shapes room.

Geometry Elements

Many elements of Geometry, but only divided into 3 main ones, namely:

• First, Point is a place (position) in space, and has a length and does not have a thickness.
• Second, Line is the set of points that have length and no width.
• Third, Field is a surface where a line joins 2 points on the surface.

Geometry Formula

For the Geometry formula itself, it is only simple, so don't be fooled by questions that say there are some geometric formulas that are complicated, geometry can also be symbolized by "r". Here's the geometric formula:

There are many formulas for geometric sequences, here's the formula for finding the Un term:

Un = ar^n-1

As for the formula to find the term Sn:

Sn = a (1 – rn)/(1 – r)

Examples of Geometry Problems

1. There is a geometric sequence for finding the term Un. Find and calculate the 10th term Un from the sequence 1/8, 1/4, 1/2,…. that !

Solution:

Is known :

• = r = 1/4: 1/8 = 1/4 x 8 = 2 (ratio)

• a = 1/8

Answer:

• Un = arn – 1
• Un = 1/8. 2 (10 – 1) = 1/8. 29 = 2 – 3. 29 = 26 = 64

So, The 10th Un term is = 64 

2. An amoeba divides into 2 every 6 minutes, what is the number of amoeba after one hour if initially there are only 2 amoeba. Find and count the term Un the number of amoeba!

Solution:

Is known :

• a = 2
• r = 2
• n = (1 hour/6 minutes) + 1 = 11

Answer:

• Un = arn – 1
• Un = 2. 2 11 – 1 = 210 = 1024 pieces of amoeba

So, The Un term for finding the amoeba is = 1024 pieces of amoeba

3. There is a geometric sequence to find the term Un. Find and calculate the 7th term Un from the sequence 3, 6, 2,…. that !

Solution:

Is known :

• a = 3

• r = 2

Answer:

• Un = ar^(n-1)
• Un = 3.2^(7-1)
• U7 = 3.2^(7-1)
• U7 = 192

So, The 17th Un term is = 192 

4. There is a geometric sequence that is used to find the term Un. Find and calculate the 7th term Un from the sequences 48, 24, 12,…. that !

Solution:

Is known :

• a = 48

• r = 1/2

Answer:

• Un = ar^n-1
• Un = 48.(1/2)^n-1
• Un = 48.(1/2)^n-1
• Un = 48.(2^-1)^1-n
• Un = 3.16. (2)^1-n
• U7 = 3.2⁴ (2)^1-n
• U7 = 3.2^5-n

So, The 7th Un term is = 3.2^5-n

5. There is a geometric sequence for finding the term Un. Find and calculate the 7th term Un from the sequence 44, 24, 12,…. that !

Solution:

Is known :

• a = 44

• r = 1/2

Answer:

• Un = ar^n-1
• Un = 44.(1/2)^n-1
• Un = 44.(1/2)^n-1
• Un = 44.(2^-1)^1-n
• Un = 3.8. (2)^1-n
• U7 = 3.2³ (2)^1-n
• U7 = 3.2^4-n

So, The 7th Un term is = 3.2^4-n

6. There is a geometric sequence that is used to find the term Un. Find and calculate the 7th term Un from the sequences 42, 24, 12,…. that !

Solution:

Is known :

• a = 42

• r = 1/2

Answer:

• Un = ar^n-1
• Un = 42.(1/2)^n-1
• Un = 42.(1/2)^n-1
• Un = 42.(2^-1)^1-n
• Un = 3.4. (2)^1-n
• U7 = 3.2² (2)^1-n
• U7 = 3.2^3-n

So, The 7th Un term is = 3.2^3-n

7. There is a geometric sequence for finding the term Un. Find and calculate the 7th term Un from the sequence 58, 24, 12,…. that !

Solution:

Is known :

• a = 48

• r = 1/2

Answer:

• Un = ar^n-1
• Un = 58.(1/2)^n-1
• Un = 58.(1/2)^n-1
• Un = 58.(2^-1)^1-n
• Un = 4.16. (2)^1-n
• U7 = 4.2⁴ (2)^1-n
• U7 = 4.2^5-n

So, The 7th Un term is = 4.2^5-n

This is a complete discussion of how to calculate geometric formulas along with examples of questions and their discussion, hopefully it will be useful…

Related Formulas:

• The formula for the circumference of a rhombus
• Square Root Formula