Check whether each of the sequences given below is an arithmetic sequence. Give reasons.

For the arithmetic sequences, write the common difference also.

i) Sequence of odd numbers

ii) Sequence of even numbers

iii) Sequence of fractions got as half the odd numbers

iv) Sequence of powers of 2

v) Sequence of reciprocals of natural numbers

i) Sequence of odd numbers

→ Odd numbers are those which are not divisible by 2

i.e. 1,3,5,7…

As, can be seen from the above sequence, it is an Arithmetic Progression.

Common difference = 3-1 = 5-3 = 2

ii) Sequence of even numbers

→ Even numbers are those which are divisible by 2

I.e. 2,4,6…

As, can be seen from the above sequence, it is an Arithmetic Progression.

Common difference = 4-2 = 6-4 = 2

iii) Sequence of fractions got as half the odd numbers

→ Odd numbers are those which are not divisible by 2

i.e. 1,3,5,7…

The sequence mentioned is half the odd numbers…

I.e. 1/2, 3/2, 5/2, 7/2,…

As, can be seen from the above sequence, it is an Arithmetic Progression.

Common difference = = = 1

iv) Sequence of powers of 2

→ The sequence of powers of 2 is as follows

2¹,2²,2³,… and so on

i.e. 2,4,8,…

Difference of second and first term = 4-2 =2

Difference of third and second term = 8-4 =4

As the difference is not same, it is not an AP.

v) Sequence of reciprocals of natural numbers

→ Natural numbers are those starting from 1 with common difference as 1

Sequence of reciprocals of natural numbers is as follows –

1/1, 1/2, 1/3 , 1/4 , 1/5… and so on

Difference of second and first term = (1/2)-(1/1) = -1/2

Difference of third and second term = (1/3) – (1/2) = -1/6

As the difference is not same, it is not an AP.