Extension: Limits of Subsequences

$\lim_{n \to \infty}a_{2n} = 2a$

$\lim_{n \to \infty}a_{2n} = a$

$\lim_{n \to \infty}2a_n = 2a$

$\lim_{n \to \infty}a_n^2 = a^2$

$\lim_{n \to \infty} \frac{1}{a_n} = \frac{1}{a}$

$\lim_{n \to \infty} |a_n| = |a|$