Mathematics
Let \(V_{r}\) denote the sum of \(1^{\text{st}\text{~}}r\) terms of an
arithmetic progression (A.P.) whose \(1^{\text{st}\text{~}}\) . term is
\(r\) and the common difference is \(2r - 1\). Let
\(T_{r} = V_{r + 1} - V_{r}\) and
\(Q_{r} = T_{r + 1} - {T}_{r}\) for
\(r = 1,2,\ldots\)
The sum \(V_{1} + V_{2} + \ldots + V_{n}\) is
A
\(\frac{n}{2}(n + 1)\left( 3n^{2} - n + 1 \right)\)
B
\(\frac{n}{12}(n + 1)\left( 3n^{2} + n + 2 \right)\)
C
\(\frac{n}{2}\left( 2n^{2} - n + 1 \right)\)
D
\(\frac{1}{3}\left( 2n^{3} - 2n + 3 \right)\)
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