For what value of $\displaystyle x$; the sequence $\displaystyle x+1, 3x, 4x+2$ are in AP?

Sum of progression $\displaystyle (a+b)$, $\displaystyle (a-b)$, $\displaystyle (a-3b)...n$ term is

Find the sum of first twenty-five terms of A.P. series whose $\displaystyle n^{th}$ term is $\displaystyle \left(n+\frac{2}{5}\right)$

The first and fifth term of an A.P. of $\displaystyle 40$ terms are $\displaystyle -29$ and $\displaystyle -15$ respectively. Find the sum of all positive terms of this A.P

If the common difference of an AP equals to the first term, then the ratio of its $\displaystyle m^{th}$ term and $\displaystyle n^{th}$ term is:

Find the value of $\displaystyle 1+2+3+...+105$

The first and last terms of an arithmetic progression are $\displaystyle 5$ and $\displaystyle 905$. Sum of the terms is $\displaystyle 45,955$. The number of terms is