Question

If the numbers x-2, 4x-1 and 5x - 2 are in A.P., Find the value
of x.
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Answer 1

$\bf\color{pink}Hola!$

$\checkmark \:\: \:\tt \underline{GiveN :}\\ \\ \rightsquigarrow \tt x-2 , \:\:4x-1 \:\:\&\:\:5x-2\:\:are \:\:in \:\:AP$

$\checkmark \:\tt\:\underline{ To\:\: FinD :}\\\\\rightsquigarrow x=?$

$\tt \checkmark \:\:\underline{SolutioN :}\\\\\tt \dashrightarrow(4x-1)-(x-2)=(5x-2)-(4x-1) \:\:\bf[\because\:\: numbers \:\:are \:\:in \:\:AP]\\\\\dashrightarrow \tt 4x-1-x+2=5x-2-4x+1\\\\\dashrightarrow \tt 3x+1=x-1\\\\\therefore {\underline{\boxed{\tt{x=-1}}}}$

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Concept BoosteR :

a, b and c is in AP it means b-a=c-b

=> 2b = c+a

=> b =(a+c)/2

a, b and c is in GP it means common ratios are same

we can say b/a=c/b

b^2=ac

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