Three alternate terms of an arithmetic progression are `x + y, x -y and 2x + 3y`, then `x` = _________.

The sum of first three terms of an arithmetic progression with n terms is x and the sum of last three terms is y.Show that the sum of n terms is n/6(x+y)

The mth term of an arithmetic progression is x and nth term is y.Then the sum of the first (m+n) terms is: a.(m+n)/(2)[x-y+(x+y)/(m+n)] b.(1)/(2)[(x+y)/(m+n)+(x-y)/(m-n)]c(1)/(2)[(x+y)/(m+n)-(x-y)/(m-n)]d(m+n)/(2)[x+y+(x-y)/(m-n)]

Three positive distinct numbers x, y, z are three terms of geometric progression in an order and the numbers x + y, y + z, z + x are three terms of arithmetic progression in that order. Prove that x^x . y^y = x^y . Y^z . Z^x .

Three numbers x,y and z in arithmetic progression if x+y+z=-3 and xyz =8 then x^(2)+y^(2)+z^(2) is equal to

Three positive distinct numbers x,y,z are three terms of geometric progression in an order , and the number x+y,y+z,z+x are three terms of arithmetic progression in that order . Prove that x^(x).y^(y).z^(z)=x^(y).y^(z).z^(x)

The intersection of three lines x-y=0 ,x +2y =3 and 2x +y=6 is a

If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.

If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.