Posted by jessica on Saturday, February 16, 2013 at 7:29am.
if log x base a,log y base a and log z base a are three consecutive terms of an AP,show that x,y and z are consecutive terms of a GP

math  Reiny, Saturday, February 16, 2013 at 8:03am
let A = log_{a}x > x = a^A
let B = log_{a}y > y = a^B
let C = log_{a}z > z = a^C
but we are told that
log_{a}x , log_{a} y , and log_{a} z
form an arithmetic sequence
so A , B, and C form an arithmetic sequence
and BA = CB
do x, y, and z form a geometric sequence ?
if so , then y/x must equal z/y
y/x = a^B / a^A = a^(BA)
z/y = a^C / a^B = a^(CB)
but BA = CB. sp
y/x =z/y and x, y, z form a geometric sequence
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