Name: Patterns of Square Numbers
Uploaded: 2019-07-19
Duration: 9 min 26 s
Description: Did you know that square numbers form various patterns? The square of any odd natural number apart from 1 can be expressed as the sum of two consecutive natu...

Question

Can you recognise the pattern in each of the sequences in Table $3 ?$

Accepted Answer

$(a)$ Regular Polygons: Triangle, quadrilateral, pentagon, hexagon, (the number of sides increases by $1$ at a time). Hence it is a continuous number sequence starting from $3 .$

$(b)$ Complete graphs:

Here number of lines is as follows:

$K_{2} = 1 K_{3} = 3 K_{4} = 6 K_{5} = 10 K_{6} = 15$

$The series formed is 1, 3, 6, 10, 15, \dots \dots .$

Hence it is a triangular number sequence.

$(c)$ Stacked Squares:

The number of small squares in each:

$The series formed is 1, 4, 9, 16, 25, \dots \dots .$

Hence it is a presentation of squares numbers sequence.

$(d)$ Stacked Triangles

The number of small triangles in each:

Hence it is also a square number sequence shown by triangles.

$(e)$ Koch Snowflake

Number of sides in each becomes $4$ times.

Can you recognise the pattern in each of the sequences in Table $3 ?$

Important Questions on Patterns in Mathematics

Learn and Prepare for any exam you want !

Can you recognise the pattern in each of the sequences in Table 3?

Important Questions on Patterns in Mathematics

Learn and Prepare for any exam you want !

Can you recognise the pattern in each of the sequences in Table $3 ?$