Visualising Number Sequences

If $x=cy+bz, y=az+cx, z=bx+ay$ and $\frac{x^2}{1-K_1}=\frac{y^2}{1-K_2}=\frac{z^2}{1-K_3}$, then $K_1+K_2+K_3$ is equal to

27 is part of which of these patterns?

Which of the following is an element in the sequence of powers of 2?

Which of the following is a square number as well as a cubic number?

How many dots are there in the bottom row of the 5th figure of a triangular pattern?

Here is a sequence of natural numbers. Some of the numbers are enclosed within square brackets:

[1], 2, [3], 4, 5, [6], 7, 8, 9, [10], 11, 12, 13, 14, [15], 16, 17, 18, 19, 18, 20, [21], 22, 23, 24, 25, 26, 27, 28, 29, 30

If we write down only the numbers in brackets, which of the following patterns do they form?

Identify the pattern below.

Which of these numbers that will fit into the pattern of a triangular numbers as well as square numbers?

How many dots should be there in the next figure if the pattern below continued?

The solids in the image are made of small cubes, the number of small cubes are mentioned below for each cube. How many small cubes will be there in the next solid if the pattern continued?

How many dots should appear in the blank box below?

Find the number of dots in the next position when the sequence below is continued.

Identify the sequence below.

How many dots should be placed in the empty box to complete sequence?

What will be next element if the sequence below is continued?

There are 5 elements in the sequence below. How many dots will be there for the 6th element?