Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences

We prove that the zeros of polynomials of consecutive degree in the sequences { r n } n = 1 ∞ and { s n } n = 1 ∞ are interlacing for n ∈ N , n ⩾ 1 where r n = p n + a n q n , s n = p n + b n q n − 1 , a n , b n ≠ 0 , a n , b n ∈ R and { p n } n = 1 ∞ and { q n } n = 1 ∞ are different sequences of Laguerre (respectively Jacobi) polynomials.