Question

# If pth,qth,rth and sth terms of an A.P are in G.P, then show that (p−q)(q−r)(r−s) are also in G.P.

Solution
Verified by Toppr

#### Given,ap=a+(p−1)daq=a+(q−1)dar=a+(r−1)das=a+(s−1)dap,aq,ar,as are in G.P⇒aqap=asarconsider,aqap=araqsubtracting 1 on both sides, we get,aqap−1=araq−1aq−apar−aq=apaqa+(q−1)d−[a+(p−1)d]a+(r−1)d−[a+(q−1)d]=apaqq−rp−q=apaq............(1)now consider,araq=asarsubtracting 1 on both sides, we get,araq−1=asar−1ar−asaq−ar=araqa+(r−1)d−[a+(s−1)d]a+(q−1)d−[a+(r−1)d]=araqr−sq−r=araqFrom (1)r−sq−r=aqap............(2)From (1) and (2), we have,apaq=aqapTherefore (p−q),(q−r),(r−s) are in G.P

0
Similar Questions
Q1

if pth,qth,rth and sth terms of an A.P. be in G.P., then (p - q),(q - r),(r - s) will be in

View Solution
Q2

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

View Solution
Q3

If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is

View Solution
Q4

If pth,qth,rth and sth terms of an A.P. be in G.P., then (p - q),(q - r),(r - s) will be in

View Solution
Q5

If the pth,qth,rth and sth terms of an A.P. are in G.P. then pq,qr,rs are in .........

View Solution
Solve
Guides