R D Sharma Solutions for Chapter: Arithmetic Progressions, Exercise 9: MULTIPLE CHOICE QUESTIONS (MCQs)

If the sum of $p$ terms of an$\mathrm{A}.\mathrm{P}.$ is $q$ and the sum of$q$ terms is $p$, then the sum of $p+q$ terms will be

In$\mathrm{A}.\mathrm{M}.\text{'}\mathrm{s}$ are introduced between $3$ and $17$ such that the ratio of the last mean to the first mean is $3 : 1,$ then the value of $n$ is

If $S_n$ denotes the sum of first $n$ terms of an $\mathrm{A}.\mathrm{P}.<a_n>$such that $\frac{S_m}{S_n}=\frac{m^2}{n^2},\text{ then }\frac{a_m}{a_n}=$

The first and last terms of an $\mathrm{A}.\mathrm{P}.$ are$1$ and $11$ . If the sum of its terms is $36$, then the number of terms will be

If the sum of $n$ terms of an $\mathrm{A}.\mathrm{P}.,$ $3n^2+5n$ then which of its terms is$164?$

If the sum of $n$ terms of an$\mathrm{A}.\mathrm{P}. is 2n^2+5n,$ then its $n$th term is

If $a_1, a_2, a_3, \dots , a_n\text{ are in A.P. }$with common difference $d$, then the sum of the series $\sin d$$\left[cosec{a}_{1}cosec{a}_2+cosec{a}_{2}cosec{a}_3+\dots .+cosec{a}_{n-1}cosec{a}_n\right]\text{ is }$

In the arithmetic progression whose common difference is non-zero, the sum of first$3n$ terms is equal to the sum of next $n$ terms. Then the ratio of the sum of the first $2n$ terms to the next $2n$ terms is