  We study the zero distribution of the sum of the first $n$ polynomials
satisfying a three-term recurrence whose coefficients are linear polynomials.
We also extend this sum to a linear combination, whose coefficients are powers
of $az+b$ for $a,b\in\mathbb{R}$, of Chebyshev polynomials. In particular, we
find necessary and sufficient conditions on $a$, $b$ such that this linear
combination is hyperbolic.
