if a,b,c are in a.p b,c,d are in gp and 1/c,1/d,1/e are in a.p prove that a,c,e are in g.p.\xa0

if a,b,c are in a.p b,c,d are in gp and 1/c,1/d,1/e are in a.p prove t

1.	if a,b,c are in a.p b,c,d are in gp and 1/c,1/d,1/e are in a.p prove that a,c,e are in g.p.\xa0
Answer» Given: b = (a + b)/2. ........(i)And. c2\xa0= bd ..........(ii)And. d = 2ce/(c + e). ..........(iii)Substituting values of b and d from eq.(i) and (iii), in eq.(ii),c2\xa0= {(a + c)/2} × {2ce/(c + e)}c2\xa0= (ace + c2e)/(c + e)c3\xa0= acec2 = ae