A series is given with one term missing. Choose the correct alternative from the given ones that will complete the series. Triangle, Square, Pentagon, ?
Hexagon
Analyzing the Polygon Series Pattern
The given series is a sequence of geometric shapes: Triangle, Square, Pentagon, ?. We need to identify the pattern and find the next term that logically completes the series.
Identifying the Pattern in the Series
Let's examine the shapes given and their fundamental properties, specifically the number of sides each shape has:
- Triangle: A triangle is a polygon with 3 sides.
- Square: A square is a quadrilateral, which is a polygon with 4 sides.
- Pentagon: A pentagon is a polygon with 5 sides.
We can see a clear pattern emerging based on the number of sides:
| Shape | Number of Sides |
|---|---|
| Triangle | 3 |
| Square | 4 |
| Pentagon | 5 |
The number of sides in each consecutive shape increases by one. The sequence of the number of sides is 3, 4, 5.
Predicting the Missing Term
Following the identified pattern, the next shape in the series should be a polygon with one more side than the Pentagon. Since the Pentagon has 5 sides, the next shape should have \(5 + 1 = 6\) sides.
A polygon with 6 sides is called a Hexagon.
Evaluating the Options
Let's look at the given options and check the number of sides for each:
- Decagon: A decagon is a polygon with 10 sides.
- Heptagon: A heptagon is a polygon with 7 sides.
- Octagon: An octagon is a polygon with 8 sides.
- Hexagon: A hexagon is a polygon with 6 sides.
Comparing the required number of sides (6) with the number of sides of the shapes in the options, we find that the Hexagon has 6 sides, which fits the pattern.
Conclusion
The series follows a pattern where each term is a polygon with one more side than the previous term. Starting with a Triangle (3 sides), then a Square (4 sides), and a Pentagon (5 sides), the next term must be a polygon with 6 sides. A polygon with 6 sides is a Hexagon.
Revision Table: Polygon Series
| Term in Series | Shape | Number of Sides | Pattern Logic |
|---|---|---|---|
| 1st | Triangle | 3 | Starting point |
| 2nd | Square | 4 | 3 + 1 |
| 3rd | Pentagon | 5 | 4 + 1 |
| 4th (Missing Term) | Hexagon | 6 | 5 + 1 |
Additional Information on Polygons and Series
This question tests your ability to recognize patterns based on the properties of geometric shapes. Polygons are closed figures made up of straight line segments. They are named based on the number of sides they have.
- 3 sides: Triangle
- 4 sides: Quadrilateral (including Square, Rectangle, Rhombus, etc.)
- 5 sides: Pentagon
- 6 sides: Hexagon
- 7 sides: Heptagon
- 8 sides: Octagon
- 9 sides: Nonagon
- 10 sides: Decagon
Number series and pattern recognition questions are common in logical reasoning tests. They can involve numbers, letters, shapes, or combinations, following arithmetic progressions, geometric progressions, or other logical rules like the one shown in this polygon series example.
Important Questions from General Knowledge Series
A series is given, with one word missing, Choose the correct alternative from the given ones that will complete the series.
Retina, National, Algebra, Radiator, ?A series is given, with one word missing. Choose the correct alternative from the given ones that will complete the series.
Random, Omelette, Telephone, Nectar,?
Select the correct option that indicates the arrangements of the following words in a logical order.
i. Century
ii. Month
iii. Year
iv. Decade
v. Millennium
A series is given, with one word missing. Choose the correct alternative from the given ones that will complete the series.
Oxygen, Toil, Arouse, Arson, Tenuous, ?
Select the correct alternative from the given ones that will complete the series.
Right to freedom, Right to equality, Right against exploitation, Right to freedom of religion, cultural and educational rights?
