Question

ifa,b,c are in ap then a/bc, 1/c, 1/b are in​

Answer 1

Answer:

Step-by-step explanation:if a,b,c are in AP then a/bc, 1/c, 1/b are in​

a , b , c  are in AP

=> 2b = a + c

let say

a/bc   , 1/c  ,  1/b   are in AP

if  2/c = a/bc  + 1/b

if 2b = a  + c

Hence a/bc   , 1/c  ,  1/b   are in AP

a/bc   , 1/c  ,  1/b   are in GP

if (1/c)² = (a/bc)(1/b)

if 1/c²  = a/b²c

iff b² = ac

but 2b = a + c

Hence a/bc   , 1/c  ,  1/b   are not in GP

a/bc   , 1/c  ,  1/b   are in HP

iff  2c  = bc/a  + b

iff 2ac = bc + ab

=> b = 2ac/(a + c)

but 2b = a + c

Hence a/bc   , 1/c  ,  1/b   are not in HP

a/bc   , 1/c  ,  1/b   are in AP if if a,b,c are in AP