If pth, qth, rth, and sth term of an A.P are in G.P then (p-q), (q-r),( r-s) are in ?
My work so far:-
An algebraic approach:-
Since these terms are in G.P, hence
Unable to move further on the above fraction. It's a huge expression and I am unable to express it into lowest terms.
Next, p-q= a+(p-1)d - [a+(q-1)d] = p-q.
Similarly we get q-r=q-r and r-s=r-s.
But, how do we prove that (p-q),(q-r) and (r-s) are in G.P algebraically.
[Request an algebraic solution]