Patterns in Numbers

Start with a number, if it is even divide it by $2$, if it is odd multiply by $3$ and add $1$. Do all starting numbers eventually reduce to $1$?

Write three consecutive integers which are odd and precedes $8$

Given that ;

$1^2+2^2=\frac{2\times 3\times 5}{6}, 1^2+2^2+3^2=\frac{3\times 4\times 7}{6}, 1^2+2^2+3^2+4^2=\frac{4\times 5\times 9}{6} \mathrm{etc}$

Using the above pattern, determine ${\left(10\right)}^2+{\left(11\right)}^2+{\left(12\right)}^2+{\left(13\right)}^2+.........+{\left(50\right)}^2$

Find the next number of the fibonacci sequence $0, 1, 1, 2, 3, 5, 8, 13, 21, 34$.

$15$ is a triangular number.

Identify the triangular number among the given numbers: $5,11,21,25,30$

The next numbers of the pattern $43, 45, 47,$ _____

The next numbers of the pattern $24, 26, 28,$ _____

If you are on diet and have breakfast consisting of $190$ calories, a lunch consisting of $350$ calories, and a dinner consisting of $1000$ calories, then find the sum of the calories consumed that day. [Write the answer in calories.]

If you are on diet and have breakfast consisting of $180$ calories, a lunch consisting of $350$ calories, and a dinner consisting of $1000$ calories, then find the sum of the calories consumed that day. [Write the answer in calories.]

If you are on diet and have breakfast consisting of $170$ calories, a lunch consisting of $350$ calories, and a dinner consisting of $1000$ calories, then find the sum of the calories consumed that day. [Write the answer in calories.]

If you are on diet and have breakfast consisting of $160$ calories, a lunch consisting of $350$ calories, and a dinner consisting of $1000$ calories, then find the sum of the calories consumed that day. [Write the answer in calories.]

If you are on diet and have breakfast consisting of $150$ calories, a lunch consisting of $350$ calories, and a dinner consisting of $1000$ calories, then find the sum of the calories consumed that day. [Write the answer in calories.]

The next number of the given fibonacci sequence is $0, 1, 1, 2, 3, 5, 8, 13, 21, 34$ is _____

Write the first $10$ square numbers. What do you notice about the way the list of numbers grows?

Which is the even number ?

$$\begin{gathered} 1^3 = 1^2 \\ {1}^3+2^3 = {\left(1+2\right)}^2={\left(3\right)}^2 \\ {1}^3+2^3+3^3 = {\left(1+2+3\right)}^2={\left(6\right)}^2 \\ {1}^3+2^3+3^3+4^3 = {\left(\_\_\_\_\right)}^2 \\ .................... = {\left(1+2+3+.....+10\right)}^2 \end{gathered}$$

Hence, we can generalise that,

The sum of the cubes of first $\text{'}n\text{'}$ natural numbers is equal to the square of their sum.

 $23$ is a natural number.

 $0$ is a natural number.

Fill in the blank with correct symbol $>, <, =$.

$99876$ _____ $99786$