Sequence of linear functionals

There is the sequence of lienar functionals $\phi_n:X\rightarrow\mathbb{R}$, $n=0,1,\dots$ on the Banach space $X$ for which the map:$$\Phi:X \ni x\rightarrow(\phi_n(x))_{n=0}^{\infty}\in \ell^{1}$$is well defined.

Prove that $\Phi$ is continuous $\iff$ $\phi_n$ is continuous for $n=0,1,\dots$

Thanks for any help.