Question

Find the value of x for which (5x+2),(4x - 1) and (x+2) are in AP.
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Answer 1

Hey Buddy

Here's The Answer

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If a, b, c is in A.P. then their common difference should be same,i.e

b - a = c - a

Using same rule in the given question

( 5x + 2 ), ( 4x - 1 ), ( x + 2 )

=> ( 4x - 1 ) - ( 5x + 2 ) = ( x + 2 ) - ( 4x - 1 )

=> 4x - 1 - 5x - 2 = x + 2 - 4x + 1

=> -x - 3 = -3x + 3

=> 3x - x = 3 + 3

=> 2x = 6

=> x = 3 ✓

Let's check

=> ( 5x + 2 ), ( 4x - 1 ), ( x + 2 )

=> ( 5×3 + 2 ), ( 4×3 - 1 ), ( 3 + 2 )

=> 17, 11, 5

==> 11 - 17 = - 6

==> 5 - 11 = -6

Hence, x = 3 for ( 5x + 2 ), ( 4x - 1 ), ( x + 2 ) to be in A.P.

Hope It Helps.