If the sum of $n$ terms of a sequence is $S_n = 3n^2 + 4n$,then what type of sequence is it?

The sum of $n$ arithmetic means between $a$ and $b$ is:

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

When the $9^{th}$ term of an $A.P.$ is divided by its $2^{nd}$ term,the quotient is $5$. When the $13^{th}$ term is divided by the $6^{th}$ term,the quotient is $2$ and the remainder is $5$. Find the first term of the $A.P.$

Suppose we have an arithmetic progression $a_1, a_2, \ldots, a_n, \ldots$ with $a_1 = 1$ and $a_2 - a_1 = 5$. The median of the finite sequence $a_1, a_2, \ldots, a_k$,where $a_k \leq 2021$ and $a_{k+1} > 2021$,is

The common difference of the $A.P.$ $b_{1}, b_{2}, \ldots, b_{m}$ is $2$ more than the common difference of $A.P.$ $a_{1}, a_{2}, \ldots, a_{n}$. If $a_{40} = -159$,$a_{100} = -399$ and $b_{100} = a_{70}$,then $b_{1}$ is equal to: