If the pth, qth and rth terms of a G.P. are , l,m,n respectively , then `l^(q-r)m^(r-p)n^(p-q)` is `:`

The fourth seventh and tenth terms of a G.P. are p,q,r respectively, then :

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

The sum of the first three terms of an A.P is 33 . If the product of the first terms and third term exceeds the 2nd term by 29 then find the A.P . The pth qth and rth term of an A.P . Are a b and c respectively . Prove that a (q-r)+ b(r-P)+c(p-q)=0

If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and c, respectively. Prove that a^(q – r) b^(r-p) c^(P - q) = 1.

If pth, qth and rth terms of a HP be respectively a,b and c , has prove that (q-r)bc+(r-p)ca+(p-q)ab=0 .

The 5th ,8th , 11th , terms of a G.P. are p,q and s, respectively .Show that q^(2) =ps

l,m,n are the pth , qth rth terms of a G.P. (all positive) , then |(log l,p,1),(logm,q,1),(logn,r,1)| equals :

If the first and the n^("th") term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P^2 = (ab)^n .

If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

T_p,T_q,T_r are the pth , qth and rth terms of an A.P., then |(T_p,T_q,T_r),(p,q,r),(1,1,1)| equals :