Mean Value and Variance-Brownian motion

Let n>=1, times 0=t₀<t₁<...<t_n, constants a₁,a₂,...,a_n ε R. Show that the random variable a₁B(t₁)+...+a_nB(t_n) is normally distributed and find its mean value and variance. (B is a brownian motion)

Since B is a Brownian Motion, E(B(t)-B(s))=0, s<t, and B(0)=0, can we say that E(a₁B(t₁)+...+a_nB(t_n))=E(a₁(B(t₁)-B(t₀)))+...+E(a_n(B(t_n)-B(t₀)))=0 ???
And how can I find Var(a₁B(t₁)+...+a_nB(t_n))????