Let V$$_r$$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ($$2r-1$$). Let $${T_r} = {V_{r + 1}} - {V_r} - 2$$ and $${Q_r} = {T_{r + 1}} - {T_r}$$ for r = 1, 2, ...

The sum V$$_1$$ + V$$_2$$ + ... + V$$_n$$ is

Let V$$_r$$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ($$2r-1$$). Let $${T_r} = {V_{r + 1}} - {V_r} - 2$$ and $${Q_r} = {T_{r + 1}} - {T_r}$$ for r = 1, 2, ...

T$$_r$$ is always

Let V$$_r$$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ($$2r-1$$). Let $${T_r} = {V_{r + 1}} - {V_r} - 2$$ and $${Q_r} = {T_{r + 1}} - {T_r}$$ for r = 1, 2, ...

Which one of the following is a correct statement?

Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents to the parabola at P and Q intersect the x-axis at S.

The ratio of the areas of the triangles PQS and PQR is