Arithmetic Progression (A.P.)

Two A.P.s have the same common difference. The first term of one of these is $-1$ and that of the other is $-8$. Then the difference between their $4^{\mathrm{th}}$ terms is

What is the common difference of an A.P. in which $a_{18}-a_{14}=32$?

If the common difference of an A.P. is $5$, then what is $a_{18}-a_{13}$?

The first four terms of an A.P., whose first term is $-2$ and common difference is $-2$ are

The list of numbers $-10,$ $-6,$ $-2,$ $2,$ ... is

In an A.P., if $d=-4,$ $n=7,$ $a_n=4$, then $a$ is

Is the given A.P. $2,$ $\frac{5}{2},$ $3,$ $\frac{7}{2},$ ... , form an A.P. If yes, find $5^{\mathrm{th}}$ term.

Find the common difference of the A.P. $-5,$ $-1,$ $3,$ $7,$...

The difference of consecutive terms of an A.P. is always a _____. (constant / inconstant)

For an A.P. $\left\{a_n\right\}$, the quantity $a_n$_____$a_{n-1}$ is called the common difference.

The total number of two digit numbers divisible by $8$ is _____.

We can find an A.P. with zero common difference.

$\sqrt{3},$ $\sqrt{12},$ $\sqrt{21},$ $\sqrt{30},$ ... form an A.P.

In an A.P., sum of the terms equidistant from beginning and end is always same and is equal to sum of the first and the last terms.

The $2\mathrm{nd}$, $31\mathrm{st}$ and last terms of an A.P. are $7\frac{3}{4},\frac{1}{2}$ and $-6\frac{1}{2}$ respectively, find the first term and the number of terms.

The fourth term of an A.P. is equal to $3$ times the first term and seventh term exceeds twice the third term by $1$. Find the first term and the common difference.

In an $\mathrm{A}.\mathrm{P}.$, the $m\mathrm{th}$ term is $\frac{1}{n}$ and $n\mathrm{th}$ term is $\frac{1}{m}$, find the $\left(mn\right)\mathrm{th}$ term.

Find the number of all three-digit natural numbers which are divisible by $9$?

Is the sequence $1^2, 3^2, 5^2, 7^2,...$ an A.P.? $($Yes$/$No$)$

Write three terms of the A.P. whose first term, $a=10$ and common difference, $d=5$.