Question

lf the pth term qth term and rth term of an ap is x y z respectively x(q_r) +Y(r_p)+Z(p_q)=0​

Answer 1

So we have,

a + (p - 1)d = x → (1)

a + (q - 1)d = y → (2)

a + (r - 1)d = z → (3)

By subtracting (2) from (1), we get,

p - q = (x - y) / d

By subtracting (3) from (2), we get,

q - r = (y - z) / d

By subtracting (1) from (3), we get,

r - p = (z - x) / d

Now,

x(q - r) + y(r - p) + z(p - q)

= x(y - z) / d + y(z - x) / d + z(x - y) / d

= [x(y - z) + y(z - x) + z(x - y)] / d

= [xy - xz + yz - yx + zx - zy] / d

= 0

Hence Proved!