Find the sum of the following:

$2+4+6+........+100$

Find the sum of the following:

$3+7+11+........+199$

If the terms of the arithmetic sequence $\frac{2}{9},\frac{3}{9},\frac{4}{9},\frac{5}{9}.......$ are represented as $x_1,x_2,x_3 .......$ then $x_1+x_2+x_3=$ _____

If the terms of the arithmetic sequence $\frac{2}{9},\frac{3}{9},\frac{4}{9},\frac{5}{9}.......$ are represented as $x_1,x_2,x_3 .......$ then $x_4+x_5+x_6=$ _____

If the terms of the arithmetic sequence $\frac{2}{9},\frac{3}{9},\frac{4}{9},\frac{5}{9}.......$ are represented as $x_1,x_2,x_3 .......$ then find the sum of first $9$ terms.

If the terms of the arithmetic sequence $\frac{2}{9},\frac{3}{9},\frac{4}{9},\frac{5}{9}.......$ are represented as $x_1,x_2,x_3 .......$ then what is the sum of first $300$ terms?

Read the following. Understand mathematical concepts in it and answer the questions that follow. The remainders obtained on dividing the powers of two by $7$ have an interesting property. We can understand it from the table given below. 

If the powers are $1, 4, 7 \dots ..$ the remainder is $2$.
If the powers are $3, 6, 9 \dots ..$ the remainder is $1$.
What is the remainder on dividing $2^8$ by $7$?

Read the following. Understand mathematical concepts in it and answer the questions that follow. The remainders obtained on dividing the powers of two by $7$ have an interesting property. We can understand it from the table given below. 

If the powers are $1, 4, 7 \dots ..$ the remainder is $2$.
If the powers are $3, 6, 9 \dots ..$ the remainder is $1$.

Write the sequence of powers of $2$ leaving remainder $1$ on division by $7$.

Read the following. Understand mathematical concepts in it and answer the questions that follow. The remainders obtained on dividing the powers of two by $7$ have an interesting property. We can understand it from the table given below. 

If the powers are $1, 4, 7 \dots ..$ the remainder is $2$.
If the powers are $3, 6, 9 \dots ..$ the remainder is $1$.

Check whether $2019$ is a term of arithmetic sequence $3, 6, 9 \dots \dots .$