R D Sharma Solutions for Chapter: Arithmetic Progressions, Exercise 2: EXERCISE 19.2

If $k^{\mathrm{th}}$ term of the A.P. $4, \mathrm{9,} 14, ...$ is $254$, then find $k$.

Find the ${12}^{\mathrm{th}}$ term from the end of the following arithmetic progression:

$\mathrm{3,5},\mathrm{7,9},\dots 201$.

Find the ${12}^{\mathrm{th}}$ term from the end of the following arithmetic progression.

 $\mathrm{3,} 8, 13, ..., 253$ .

Find the ${12}^{\mathrm{th}}$ term from the end of the following arithmetic progression.

 $\mathrm{1,} 4, \mathrm{7,} 10, ... 88$.

 An A.P consists of $60$ terms. If the first and the last terms be $7$ and $125$ respectively, find ${32}^{\mathrm{nd}}$ term.

The sum of $4^{\mathrm{th}}$ and $8^{\mathrm{th}}$ terms of an A.P is $24$ and the sum of the  $6^{\mathrm{th}}$ and ${10}^{\mathrm{th}}$ terms is $34$. Find the first term and the common difference of the A.P.

How many numbers are there between $1$ and $1000$ which when divided by $7$ leave remainder $4$?

If an A.P. is such that $\frac{a_4}{a_7}=\frac{2}{3}$, find $\frac{a_6}{a_8}.$