If $S_n$ denotes the sum of $n$ terms of an arithmetic progression,then the value of $(S_{2n} - S_n)$ is equal to

If the roots $\alpha, \beta, \gamma$ of the equation $x^3-6x^2+px+10=0$ are in arithmetic progression,then $\alpha^3+\beta^3+\gamma^3=$

If $\frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}$ is the $A.M.$ between $a$ and $b,$ then find the value of $n$.

Jairam purchased a house for Rs. $15000$ and paid Rs. $5000$ at once. He promised to pay the remaining amount in annual installments of Rs. $1000$ with $10\%$ per annum interest on the outstanding balance. How much total money will be paid by Jairam in Rs.?

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 sum of the first $n$ terms of an $A.P.$ is $cn(n - 1)$,where $c \neq 0$,then the sum of the squares of these terms is: