Question

a b c are in the ap if the value of a+ b by 2 = x and b+ c by 2 = y then find the value of x + y​

Answer 1

The value of x + y = 2b

Given :

a , b , c are in AP

$\displaystyle \sf{ \frac{a + b}{2} = x \: \: and \: \: \frac{b + c}{2} = y}$

To find :

The value of x + y

Solution :

Step 1 of 2 :

Find the relation between a , b , c

Here it is given that a , b , c are in AP

∴ Common difference exists

⇒ b - a = c - b

⇒ 2b = a + c

Step 2 of 2 :

Find the value of x + y

$\displaystyle \sf{ \frac{a + b}{2} = x \: \: and \: \: \frac{b + c}{2} = y}$

Thus we get ,

$\displaystyle \sf{ x + y }$

$\displaystyle \sf{ = \frac{a + b}{2} + \frac{b + c}{2} }$

$\displaystyle \sf{ = \frac{a + b + b + c}{2} }$

$\displaystyle \sf{ = \frac{a + c + 2b }{2} }$

$\displaystyle \sf{ = \frac{2b + 2b }{2} }$

$\displaystyle \sf{ = \frac{4b }{2} }$

$\displaystyle \sf{ = 2b }$

Hence the required value of x + y = 2b

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