if a,b,c are in AP then a/bc, 1/c, 2/b are in
Answers
They are in HP.... .. ..
a/bc , 1/c , 1/b are in AP if if a,b,c are in AP
Step-by-step explanation:
correct Question :
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
iff 2/c = a/bc + 1/b
iff 2b = a + c
Hence a/bc , 1/c , 1/b are in AP
a/bc , 1/c , 1/b are in GP
iff (1/c)² = (a/bc)(1/b)
iff 1/c² = a/b²c
iff 1/c = a/b²
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
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