if a, b, c are in A.P, then show that 1) b+c, c+a, a+b are also in A.P.
Answers
Answered by
36
a , b , c are in A.P.
We know, 2 × middle term = sum of remaining two.
So,
➡ 2 × b = a + c
➡ 2b = a + c -------: ( 1 )
If b + c , c + a , a + b are also in A.P.
2 × ( c + a ) = b + a + b + c is true
Or, 2 × ( c + a ) = c + a + b + b is true
Or, 2 × ( c + a ) = c + a + 2b is true

Or, 2 × ( 2b ) = 2b + 2b is true
Or, 4b = 4b is true
0 = 0
Hence, both are equal. It means that b + c , c + a , a + b are in A.P.
We know, 2 × middle term = sum of remaining two.
So,
➡ 2 × b = a + c
➡ 2b = a + c -------: ( 1 )
If b + c , c + a , a + b are also in A.P.
2 × ( c + a ) = b + a + b + c is true
Or, 2 × ( c + a ) = c + a + b + b is true
Or, 2 × ( c + a ) = c + a + 2b is true
Or, 2 × ( 2b ) = 2b + 2b is true
Or, 4b = 4b is true
0 = 0
Hence, both are equal. It means that b + c , c + a , a + b are in A.P.
abhi569:
(-:
Answered by
21
❤❤Here is your answer ✌ ✌

a,b,c are in ratio
We know, 2 × middle term = sum of remaining two.
So,
➡ 2 × b = a + c
➡ 2b = a + c -------: ( 1 )
If b + c , c + a , a + b are also in A.P.
2 × ( c + a ) = b + a + b + c is true
Or, 2 × ( c + a ) = c + a + b + b is true
Or, 2 × ( c + a ) = c + a + 2b is true
Putting the value from(1)
Or, 2 × ( 2b ) = 2b + 2b is true
Or, 4b = 4b is true
0 = 0
Hence, both are equal. It means that b + c , c + a , a + b are in A.P
a,b,c are in ratio
We know, 2 × middle term = sum of remaining two.
So,
➡ 2 × b = a + c
➡ 2b = a + c -------: ( 1 )
If b + c , c + a , a + b are also in A.P.
2 × ( c + a ) = b + a + b + c is true
Or, 2 × ( c + a ) = c + a + b + b is true
Or, 2 × ( c + a ) = c + a + 2b is true
Putting the value from(1)
Or, 2 × ( 2b ) = 2b + 2b is true
Or, 4b = 4b is true
0 = 0
Hence, both are equal. It means that b + c , c + a , a + b are in A.P
Similar questions