Make the following number sequences from the sequence of equilateral triangles, squares, regular pentagons and so on, of regular polygons.

Number of sides – 3,4,5…

Sum of interior angles –

Sum of exterior angles –

One interior angle –

One exterior angle –

For the following sequences, let

a = First term of sequence

d = common difference if the sequence is an AP

a) Number of sides – 3,4,5,6,7…. And so on is an Arithmetic Progression.

Where a = 3 and d = 1

b) Sum of interior angles of a regular polygon with n sides = (n-2)×180

Putting n = 3, 4, 5, 6… and so on

The required sequence is 180,360,540,720… and so on.

An AP with a = 180 and d = 180

c) Sum of exterior angles of any closed polygon is 360

Hence the sequence is 360,360,360… and so on i.e. AP with a = 360 and d = 0

d) One Interior angle = (Sum of all interior angles)/(No. of sides)

=

Putting n = 3, 4, 5… and so on…

The sequence is 60, 90, 108, 120… and so on. Here, the sequence is not an AP

e) One exterior angle =

(∵ no. of exterior angles = no. of sides)

=

Putting n = 3, 4, 5… and so on

The sequence is 120, 90, 72, 60… and so on which is clearly not an AP.