R. D. Sharma Solutions for Chapter: Arithmetic Progression, Exercise 4: EXERCISE 5.4

Which term of the A.P. $4, 9, 14,\dots$ is $254?$

How many terms are there in the A.P.$?$

$-1, -\frac{5}{6}, -\frac{2}{3}, -\frac{1}{2},\dots , \frac{10}{3}$.

How many terms are there in the A.P.?

$7, 13, 19,\dots ,205$

If an AP consists of $n$ terms with first term $a$ and $n^{\mathrm{th}}$ term $l$, show that the sum of the $m^{\mathrm{th}}$ term from the beginning and the $m^{\mathrm{th}}$ term from the end is $(a+l)$.

How many numbers lie between $10$ and $300$, which when divided by $4$ leaves a remainder $3?$

Find the ${12}^{th}$ term from the end of the $A.P$. $-2, -4, -6, \dots \dots .,-100$.

For the $A.P$. $-3, -7, -11, \dots \dots .$ can we find $a_{30}-a_{20}$ without actually finding $a_{30}$ and $a_{20}$? Give reasons for your answer.

Two $A.P$.s have the same common difference. The first term of one$A.P$. is $2$ and that of the other is $7$. The difference between their ${10}^{\mathrm{th}}$ terms is the same as the difference between their ${21}^{\mathrm{st}}$ terms, which is the same as the difference between any two corresponding terms. Why$?$