If pth,qth, rth and sth terms of an A.P. are in G.P., show that p-q,q-r,r-s are also in G.P.

If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G.P.

If the (m+1)t h ,(n+1)t h ,a n d(r+1)t h terms of an A.P., are in G.P. and m ,n ,r are in H.P., then find the value of the ratio of the common difference to the first term of the A.P.

The pth, (2p)th and (4p)th terms of an AP, are in GP, then find the common ratio of GP.

If agt0,bgt0,cgt0 be respectively the pth, qth and rth terms of a G.P. are a, b ,c , prove that : (q-r) log a+ (r -p) log b + (p -q) log c = 0 .

If the pth, qth and rth terms of an A.P. be x,y,z repsectively, then show that : x(q-r)+y(r-p)+z(p-q)=0

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 + (p- q)c= 0

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

If the 2nd , 5th and 9th terms of a non-constant A.P are in G.P then the common ratio of this G.P is

If ‘a’ and ‘b’ are respectively the pth and qth terms of an A.P., show that the sum of (p + q) terms is (p+q)/2[(a + b) + (a- b)/(p - q)] .

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 .