If $\log _{3} 2, \log _{3}(2^{x}-5), \log _{3}(2^{x}-\frac{7}{2})$ are in an arithmetic progression,then the value of $x$ is equal to $.....$

If the $p^{th}$ term of an arithmetic progression is $q$ and its $q^{th}$ term is $p$,then what is its $(p + q)^{th}$ term?

If $\frac{S_n}{S_m} = \frac{n^4}{m^4}$ (where $S_k$ is the sum of the first $k$ terms of an $A$.$P$. $a_1, a_2, \dots$),then the value of $\frac{a_{m+1}}{a_{n+1}}$ in terms of $m$ and $n$ is:

If $\log 2, \log (2^n - 1)$ and $\log (2^n + 3)$ are in $A.P.$,then $n =$

Statement-$I$: If the ratio of the sum of $n$ terms of two arithmetic progressions is $(7n + 1) : (4n + 17)$,then the ratio of their $n^{th}$ terms is $7 : 4$.
Statement-$II$: If $S_n = an^2 + bn + c$,then $T_n = S_n - S_{n-1}$.

In an arithmetic progression,if $T_m = n$ and $T_n = m$,then $T_p = \dots$