Math Snap

STEP 1

Assumptions1. The sequence is defined by the formula $^{n+1}$
. The table provides the first five terms of the sequence3. We need to find the limit of the sequence as $n$ approaches infinity

STEP 2

First, let's write down the general term of the sequence using the given formula.
$$a_n =2^{n+1}$$

STEP 3

Now, we need to find the limit of the sequence as $n$ approaches infinity.
$$\lim{n \rightarrow \infty} a_{n} = \lim{n \rightarrow \infty}2^{n+1}$$

We know that for any positive constant $k$, $\lim{n \rightarrow \infty} k^n = \infty$. Here, $k =2$ is a positive constant. Therefore, the limit of the sequence as $n$ approaches infinity is infinity.
$$\lim{n \rightarrow \infty}2^{n+1} = \infty$$The correct choice is B. The limit does not exist or is $\infty$ or $-\infty$.