$11^2 + 12^2 + 13^2 + \dots + 20^2 = $

The first term of an infinite geometric progression is $x$ and its sum is $5$. Then:

The sum to infinity of a geometric progression is $4/3$ and the first term is $3/4$. The common ratio is

Consider a sequence whose sum of first $n$ terms is given by $S_n = 4n^2 + 6n$,where $n \in N$. Find the $15^{th}$ term $(T_{15})$ of this sequence.

If $|\alpha| < 1$ and $|\beta| < 1$,where $s_1 = 1 - \alpha + \alpha^2 - \alpha^3 + \dots \infty$ and $s_2 = 1 - \beta + \beta^2 - \beta^3 + \dots \infty$,then $1 - \alpha\beta + \alpha^2\beta^2 - \alpha^3\beta^3 + \dots \infty$ equals:

If the $n^{th}$ term of a series is $3 + n(n - 1)$,then the sum of $n$ terms of the series is