If the series Cn 4^n is convergent, which of the following must be true

cn (−4)n is convergent

cn (−3)n is convergent

cn (−3)n is divergent

cn (−4)n is divergent

By hypothesis, the radius of convergence is at least 4.

So, Σ c(n) x^n will converge for sure when |x| < 4.
==> The series converges for x = -3.

We need more information about c(n) to discuss convergence at x = -4.
(However, if c(n) > 0, then we have absolute convergence at x = -4, since Σ c(n) 4^n converges.)

I hope this helps!