If a, b, c are respectively the `p^(th)q^(th)andr^(th)` terms of a GP. Show that `(q-r)loga+(r-p)logb+(p-q)logc=0`.

If x,y,z are respectively p^(th), q^(th) and r^(th) terms of a G.P show that x^(q-r) xx y^(r-p) xx z^(p-q)=1 .

If a,b,c are all positive, and are p^(th), q^(th) and r^(th) terms of a G.P., show that |("log"a,p,1),("log"b,q,1),("log"c,r,1)|=0 .

If a, b and c are respectively the p^(th) , q^(th) and r^(th) terms of an A.P., then |(a" "p" "1),(b" "q" "1),(c" "r" "1)|=

If a gt 0, b gt 0, c gt0 are respectively the pth, qth, rth terms of a G.P., then the value of the determinant |(log a,p,1),(log b,q,1),(log c,r,1)| , is

The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectively. Show that (q-r) a+(r-p) b+(q-p)c = 0

If p^(th), q^(th) and r^(th) terms of an A. P. are l, m, n, respectively, show that (q - r )l + (r -p)m +(p - q)n =0

If a,b,c are p^(pt),q^(th) and r^(th) terms of an A.P., find the value of |(a,b,c),(p,q,r),(1,1,1)| .