Here is fun with triangular numbers. First complete the list and then write them in the table as shown.

$1, 3, 6, 10$, _____ , _____ , _____ , $36, 45$.

$1$	$3$	$6$	$10$				$36$
	$1$	$3$	$6$	$10$				$36$

Now add them together and write the sum in the bottom row.

What can you say about the numbers formed in this row?

Write your conclusion in the form of a statement.

In the question given below, the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

Which number will replace the question mark?

In the question given below, the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

Select the combination of letters that when sequentially placed in the blanks of the given series will complete the series.

$\mathrm{l} \mathrm{\_} \mathrm{chtlgc} \mathrm{\_} \mathrm{tlg} \mathrm{\_} \mathrm{ht} \mathrm{\_} \mathrm{gc} \mathrm{\_} \mathrm{tlgch} \mathrm{\_}$

If, in a two-digit number, the digit at unit place is $x$ and the digit at tens place is $4$, then the two-digit number is _____.

Consider a three-digit number with the following properties:

I. If its digits in units place and tens place are interchanged, the number increases by $36$
II. If its digits in units place and hundreds place are interchanged, the number decreases by $198$ .

Now, suppose that the digits in tens place and hundreds place are interchanged. Then, the number

Let ${\left\{a_n\right\}}_{n=0}^{\infty }$ be a sequence such that $a_0=a_1=0$ and $a_{n+2}=3a_{n+1}-2a_n+1,\forall n\ge 0$.

Then $a_{25}{a}_{23}-2a_{25}{a}_{22}-2a_{23}{a}_{24}+4a_{22}{a}_{24}$ is equal to

In the question given below, the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

Let $<a_n>$ be a sequence such that $a_1+a_2+...+a_n=\frac{n^2+3n}{\left(n+1\right)\left(n+2\right)}$. If $28\sum _{k=1}^{10}\frac{1}{a_k}=p_1 p_2 p_{3 }... p_m$, where $p_1, p_2, ... p_m$ are the first $m$ prime numbers, then $m$ is equal to

Which number will replace the question mark?