Kerala Board Solutions for Chapter: Arithmetic Sequences, Exercise 4: Exercise 4

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.

The algebraic expression of a sequence is $x_n=n^3–6n^2+13n–7$. Is it an arithmetic sequence?