Let $\left\{a_{n}\right\}$ be a sequence of real numbers. Which of the following is true?
- If $\sum a_{n}$ converges, then so does $\sum a_{n}^{4}$
- If $\sum |a_{n}|$ converges, then so does $\sum a_{n}^{2}$
- If $\sum a_{n}$ diverges, then so does $\sum a_{n}^{3}$
- If $\sum |a_{n}|$ diverges, then so does $\sum a_{n}^{2}$