Check whether the sequence given below is an arithmetic sequence. Give reasons. For the arithmetic sequences, write the common difference also.

Sequence of reciprocals of natural numbers.

Look at these pictures:

If the pattern is continued, do the numbers of coloured squares form an arithmetic sequence?

See the pictures below:

How many small blue squares are there in each rectangle? Is the sequence of numbers, an arithmetic sequence?

See the pictures below:

How many large squares? Is the sequence of numbers, an arithmetic sequence?

See the pictures below:

How many squares in all? Is the sequence of numbers, an arithmetic sequence?

In the staircase the height of the first step is $10$ centimetres and the height of each step after it is $17.5$ centimetres.

How high from the ground would be someone climbing up, after each step? 

In the staircase the height of the first step is $10$ centimetres and the height of each step after it is $17.5$ centimetres.

How high from the ground would be someone climbing up, after each step? Write these numbers as a sequence

In this picture, the perpendiculars to the bottom line are equally spaced. Prove that, continuing like this, the lengths of perpendiculars form an arithmetic sequence.