Question

if a,b,c be in HP then ​

Answer 1

Answer:

a, b, c are in HP

Then

a

1

,

b

1

,

c

1

are in AP

⇒

c

1

−

b

1

−

b

1

−

a

1

⇒

bc

b−c

=

ab

a−b

⇒

bc

ab

=

b−c

a−b

⇒

b−c

a−b

=

c

a

.

Answer 2

Step-by-step explanation:

If a, b, c are in HP , then

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

then,

common difference = 1/b - 1/a = 1/c - 1/b

=> 2/b = 1/a + 1/c = ( a + c ) / ac

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