`S_(1),S_(2)` and `S_(3)` are the different sizes of windows 1,2 and 3 respectively placed in avertical plane. A particle is thrown up in that vertial plane, find the correct options:

W_(1),W_(2) and W_(3) are the different sizes of windows 1, 2, and 3 respectively placed in a vertical plane. A particle is thrown up in the vertical plane. Let t_(1),t_(2) and t_(3) are the time taken to cross the window W_(1), W_(2) and W_(3) respectively and DeltaV_(1), DeltaV_(2) and DeltaV_(3) are the change in speed after respective window cross.

If s_(1),s_(2)and s_(3) are the sum of first n , 2n, 3n terms respectively of an arithmetical progression , then show that s_(3)=3 (s_(2)-s_(1))

If s_(1),s_(2)and s_(3) are the sum of first n , 2n, 3n terms respectively of an arithmetical progression , then show that s_(3)=3 (s_(2)-s_(1))

If S_(1), S_(2), S_(3) are the sums of n, 2n, 3n terms respectively of an A.P., then S_(3)//(S_(2) - S_(1))-

Let each of the circles S_(1)-=x^(2)+y^(2)+4y-1=0 S_(1)-= x^(2)+y^(2)+6x+y+8=0 S_(3)-=x^(2)+y^(2)-4x-4y-37=0 touch the other two. Also, let P_(1),P_(2) and P_(3) be the points of contact of S_(1) and S_(2) , S_(2) and S_(3) , and S_(3) , respectively, C_(1),C_(2) and C_(3) are the centres of S_(1),S_(2) and S_(3) respectively. P_(2) and P_(3) are images of each other with respect to the line