Arithmetic Progression

What is infinite  arithmetic progression.

Show that the sequence $\log \left(a\right),\log \left(ab\right),\log \left(a{b}^2\right),\log \left(a{b}^3\right),...$ is an A.P. Find its ${16}^{th}$ term.

Find A.P., whose first term is $2$ and the common difference is $2$.

What is finite Arithmetic Progression?

If $k+2,4k-6,3k-2$ are the three consecutive terms of an A.P., then the value of $k$ is

The sum of four numbers in Arithmetic Progression is $20$ and the sum of their square is $120.$ Find the numbers.

Identify the infinite arithmetic progression from the following

Find the sum of the integers between $21 and 99$ divisible by $6$.

The sum of the first $10$ terms of an A.P. is $30$ and the sum of the next $10$ terms is $-170$. FInd the sum of the next $10$ terms following these.

The sum of the first $21$ terms of an A.P. is $28$ and that of the first $28$ terms is $21$. If one term is zero then find the sum of the preceding terms.

 The sum of the first $15$ terms and that of the first $22$ terms of an A.P. are $495$ and $1034$ respectively. Find the sum of the first $18$ terms.

The first term of an A.P. is $7$ and the sum of the first $15$ term is $420$. Find the common difference of the A.P.

The ${12}^{th}$ term of an A.P. is $-13$ and the sum of the first four terms is $24$. Find the sum of the first $10$ terms.

The $5^{th} and {11}^{th}$ terms of an A.P. are $41 and 20$ respectively. Find the sum of the first $12$ terms.

How many terms of the A.P. $3, 8, 13, 18, ....$ must be taken so that the sum is $1010 ?$

How many terms of the A.P. $5, 9, 13, 17, ...$ must be taken so that the sum be $1224 ?$

Find the sum of the following series:

$4+8+12+...+80$

Find the sum of the following series:

$4+7+10+ ... +49$

Find the sum of the following series:

$5+8+11+.....+47$

Find the sum of the first $40$ terms of the A.P. $10, 8, 6, 4, ...$