 Hello and welcome to this session. In this session, we are going to discuss numerical and geometrical patterns. We shall start with numerical pattern. It consists of numbers that follow a particular rule. For example, consider the following sequence of numbers 1, 4, 9, 16, 25. If we carefully analyze each number, we will be able to find the next number after 25. So, for this, we find the pattern formed by these numbers. The first number is 1, which can be written as 1 square. The next number is 4, which can be written as 2 square. Similarly, 9 can be written as 3 square. 16 can be written as 4 square and 25 can be written as 5 square. So, we observe the sequence is obtained by squaring each natural number, that is 1 square, 2 square, 3 square, 4 square, 5 square and so on. That gives the sequence 1, 4, 9, 16, 25 and so on. So, the next number in the sequence will be 36, which is obtained by squaring 6. So, the sequence now becomes 1, 4, 9, 16, 25, 36 and so on. Now, we discuss geometric pattern. A geometric pattern consists of objects, shapes, pictures, etc. that repeat themselves or change in a certain way. For example, we are given four rows consisting of red and blue squares. We want to find what the fifth row of this pattern would look like. To find it, we analyze the given rows. We see that the first row has two red squares, the second row has three blue squares, the third row has four red squares and the fourth row has five blue squares. So, we observe that in each successive row, the number of squares are increased by 1. That is, the number of squares are in the sequence 2, 3, 4, 5 and so on. Also, we observe that the color of squares in each row is also forming a particular pattern. In the first row we have red squares, in the second row we have blue squares, again in the third row we have red squares and then again we have blue squares. The pattern formed by colors is red, blue, red, blue and so on. So, from these two observations, we can find the number of squares and the color used in the fifth row. So, the fifth row will have six squares of red color. Let us consider one more example. Look at the following pattern and draw the next figure. If we observe all the figures, we see that the first figure is a triangle with three sides, the second figure is having four sides, the third figure is having five sides and the fourth figure is having six sides. Thus, the next figure will have seven sides. So, we will draw a figure having seven sides. Thus, in this way we can identify the numerical and geometrical patterns. This completes our session. Hope you enjoyed the session.