If `x_1,x_2 …,x_(20)` are in H.P and `x_1,2,x_(20)` are in G.P then `underset(r=1)overset(19)Sigmax_rr_(x+1)`

If x_1,x_2 …,x_(20) are in H.P and x_1,2,x_(20) are in G.P then Sigma_(r=1)^(19)x_rr_(x+1)

If x_1, x_2, .. x_18 are observations sach the underset(j =1)overset(18)sum(x_j-8)= 9 and underset(j =1)overset(18)sum(x_j-8)^2 = 45 , then the standard deviation. of these observations is:

If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove that x ,a n d4,z are in H.P.

If x_1,x_2,x_3 as well as y_1, y_2, y_3 are in G.P. with same common ratio, then prove that the points (x_1, y_1),(x_2,y_2),a n d(x_3, y_3) are collinear.

If x_1,x_2,x_3 as well as y_1, y_2, y_3 are in G.P. with same common ratio, then prove that the points (x_1, y_1),(x_2,y_2),a n d(x_3, y_3) are collinear.

If p_(1)^(x_(1))timesp_(2)^(x_(2))timesp_(3)^(x_(3))timesp_(4)^(x_(4))=11340 where p_(1), p_(2), p_(3), p_(4) are primes in ascending order and x_(1), x_(2), x_(3), x_(4) are integers, find the value of p_(1), p_(2), p_(3), p_(4) and x_(1), x_(2), x_(3), x_(4) .

Let x_(1), x_(2), …… , x_(n) be in an A.P. If x_(1) + x_(4) + x_(9) + x_(11) + x_(20) + x_(22) + x_(27) + x_(30) = 272 , then x_(1) + x_(2) + x_(3) + ...... + x_(30) is equal to

If f(a) = 2, f'(a) = 1, g(a) = -1, g' (a) = 2 . Then underset(x rarr a)(lim) (g (x) f(a) - g(a) f(x))/(x -a) is

If a,b,c are in G.P and a^(1/x) = b^(1/y) = c^(1/z) , prove that x,y,z are in A.P.

If both (x-2) and (x - (1)/(2)) are fractors of p x ^(2) 5x +r, then show that p=r.