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Question

# If pth, qth, rth and sth terms of an A.P are in G.P then p−q,q−r,r−s are in G.P.TrueFalse

A
True
B
False
Solution
Verified by Toppr

#### As pth,qth,rth & sth terms are in G.P∴pq=qr=rsOR pr=q2;r2=qs & ps=qrso, Lets Imagine p−q,q−r & r−s are in G.P.so, p−qq−r=q−rr−sOR (p−q)(r−s)=(q−r)2pr−ps−qr+qs=q2+r2−2qras q2=pr,r2=qs & ps=qrwe getq2−qr−qr+r2=q2+r2−2qrq2+r2−2qr=q2+r2−2qrL.H.S=R.H.S∴ Our hypothesis is true.

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