J P Mohindru and Bharat Mohindru Solutions for Chapter: Arithmetic Progressions, Exercise 9: NATIONAL TALENT SEARCH EXAMINATION (NTSE)

Ratio of the sum of $n$ terms of A.P's are $(3n+8):(7n+15)$, then the ratio of their $5^{\mathrm{th}}$ terms is

If $a_1$, $a_2$, $a_3$,...,$a_n$ be in A.P., then the value of $\frac{1}{a_1{a}_2}+\frac{1}{a_2{a}_3}+\dots +\frac{1}{a_{n-1}{a}_n}$ is

If $m^{\mathrm{th}}$ term of an A.P. is $\frac{1}{n}$ and $n^{\mathrm{th}}$ term is $\frac{1}{m}$, then the sum of $mn$ term is

If the sum of $n$ term of an A.P is $3n^2-2n,$ then its $n^{\mathrm{th}}$ term is

If the first, second and last term of an A.P. are $a$, $b$ and $2a$ respectively, then its sum is:

If the ratio of the sum of $n$ terms of two distinct arithmetic progressions is given by $\frac{S_n}{{S_n}^{\text{'}}}=\frac{3n+1}{2n+1}$, then find the ratio of their $6^{\mathrm{th}}$ terms.

Find the sum of $n$ terms of an A.P. if its $a_n$ is given by: $a_n=3n-1$.

Between $1$ and $31$, $\mathrm{m}$ arithmetic means are inserted so that the ratio of the $7^{\mathrm{th}}$ and $(m-1{)}^{\mathrm{th}}$ means is $5:9$. Find the value of $m$.