Please explain how did we get this one

[SINGHAM]

If a, b, c are in AP, then the value of the determinant
|x + 2; x + 3; x + 2a|
|x + 3; x + 4; x + 2b|
|x + 4; x + 5; x + 2c|
is
(c) 2b − a − c

[kangkan]

are u sure its the ans given?i am getting 0

[kangkan]

oh...see do the matrix operation R1= R2-R1 and R2=R3- R2 ..also remember b-a=c-b..rows 1 and 2 will be equal..hence det=0
Now a+c/2=b..therefore 2b-c-a=0..hence option c

[SINGHAM]

THANKS!