Question

for what value of k are the numbers x , 2x + k, 3x + 6 are three concecutive term of an AP

Answer 1

let
a1=x
a2=2x+k
a3=3x+6
if a1,a2,a3 are in AP
a2-a1=a3-a2
2x+k-x=(3x+6)-(2x+k)
x+k=3x+6-2x-k

x+2x-3x+k+k=6
2k=6
k=6/2
k=3