Math Help - how can this be wrong?

1. how can this be wrong?

a particle is moving along a straight line with constant acceleration. in an interval of T seconds it moves D metres; in the next interval of 3T seconds it moves 9D metres. how far does it move in a further interval of T seconds?

so I calculated the acceleration pretty simply, the velocity increased by 2D/T over 3T, so the constant acceleration is 2/3DT^-2. using this I calculated the distance travelled over the next interval of T seconds as being 0.5(3 + 3 + 2/3) = 20/6 D metres
the book says 5D metres. where did i go wrong?

2. Dear furor celtica,

From $S=ut+\frac{1}{2}at^2$

$D=uT+\frac{1}{2}aT^2$

$10D=4uT+\frac{1}{2}a(4T)^2$

$10D=4(D-\frac{1}{2}aT^2)+\frac{1}{2}a(4T)^2$

By simplification, $a=\frac{D}{T^2}$ and $u=\frac{D}{2T}$

Therefore the distance traveled in the last T seconds,

$S=(\frac{D}{2T}\times{5T})+\frac{1}{2}\frac{D}{T^2 }(5T)^2-10T$

By simplification, $S=5D$

So the book is correct. You haven't considered the fact that the particle could have an initial velocity which I had taken as u.