Subscript[X, t] ==
    (1 - [Theta])*Sum[[Theta]^(k - 1)*(Subscript[P, t - k] - Subscript[P, t - k - 1]), {k, 1, t - 1}] +
     [Theta]^(t - 1)*1; Subscript[NN, t] == Subscript[X, t]/([Gamma]*[Sigma]^2);
   Subscript[M, t] == (Subscript[D, t] - (T - t - 1)*[Gamma]*[Sigma]^2*Q - Subscript[P, t])/([Gamma]*[Sigma]^2);
   E*Subscript[NN, t] + F*Subscript[M, t]**Q; u == [Mu] - 1;
   Inequality[1, Greater, [Mu], GreaterEqual, 0

RSolve[eqn,a[n],n]