Question

circles with radii 1cm,

2cm, 3cm, ....... are

drawn

a)Write down the sequence of

diameters of circles
b)Find the

sequence of circumference of circles
c)
What is the sequence of areas of the

circles
d)Check whether the above

sequences are arithmetic sequences or

not? Why?​

Answer 1

Given:

The sequence of the radii of circles is 1 cm, 2 cm, 3 cm,....

To find:

a) The sequence of the diameter of circles

b) The sequence of the circumference of circles

c) The sequence of the areas of circles

d) To check whether the sequences are in A.P or not

Calculation:

Let r = {1, 2, 3,......}

a) Diameter of the circle = 2(radius)

   => D = 2r

   => D = {2(1), 2(2), 2(3),.....}

   => D = {2, 4, 6,.....}

b) Circumference of the circle = 2πr

   => Circumference = {2π(1), 2π(2), 2π(3),.....}

   => Circumference = {2π, 4π, 6π,.....}

c) Area of the circle = πr²

   => A = πr²

   => A = {π(1)², π(2)², π(3)²,......}

   => A = {π, 4π, 9π,.....}

d) Yes, the above sequences are in arithmetic progression. The given radii are in arithmetic progression, If we multiply a constant or variable to the arithmetic progression sequence, the resulting sequence will also be in A.P