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ok this answer is very easy
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Required ratio is 2 : 3.
Step-by-step explanation:
Let first term of the AP be a( here x ) and common difference between the terms be d.
= > x = a ... ( 1 )
Second term :
= > y = a + ( 2 - 1 )d
= > y = a + d
= > y = a + d ...( 2 )
Third term :
= > 2x = a + ( 3 - 1 )d
= > 2x = a + 2d ... ( 3 )
Subtracting ( 2 ) from ( 3 ) :
= > 2x - y = ( a + 2d ) - ( a + d )
= > 2x - y = a + 2d - a - d
= > 2x - y = d
= > 2x - y = ( a + d ) - a { add. as well as sub. of a }
= > 2x - y = y - x
= > 2x + x = 2y
= > 3x = 2y
= > x / y = 2 / 3.
Required ratio is 2 : 3.
This can also be solved using 2b = a + c where b is the middle term and a & c are remaining terms.
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