If $\displaystyle (x+1)$, $3x$\displaystyle ,$(4x+2)$ are in A.P. Find the value of $x$

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+$$\displaystyle \frac{2}{5}$\right)

The first and fifth term of an A.P. of $40$\displaystyle terms are$-29$\displaystyle and$-15$ 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 $905$. Sum of the terms is $45,955$. The number of terms is