# For the series k_n=2^n+1, what is k? what is n? what is the value of k when n=5?

Nov 7, 2017

$n$ is the position of the term within the sequence
$k$ is the value of the $n$-th term

The 5th number in the sequence is $33$.

#### Explanation:

In this problem, $k$ represents the $n$-th term in the sequence.

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When $n = \textcolor{red}{1}$:

$k = {2}^{\textcolor{red}{1}} + 1 = 2 + 1 = \textcolor{b l u e}{3}$

When $n = \textcolor{red}{2}$:

$k = {2}^{\textcolor{red}{2}} + 1 = 4 + 1 = \textcolor{b l u e}{5}$

When $n = \textcolor{red}{3}$:

$k = {2}^{\textcolor{red}{3}} + 1 = 8 + 1 = \textcolor{b l u e}{9}$

When $n = \textcolor{red}{4}$:

$k = {2}^{\textcolor{red}{4}} + 1 = 16 + 1 = \textcolor{b l u e}{17}$

This is the sequence that the problem gives us: $\textcolor{b l u e}{3} , \textcolor{b l u e}{5} , \textcolor{b l u e}{9} , \textcolor{b l u e}{17.} . .$

Our job now is to find the next term in the sequence.

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We can do this by plugging in $n = \textcolor{red}{5}$, so that $k$ will be the $5$th term in the sequence.

$k = {2}^{\textcolor{red}{5}} + 1 = 32 + 1 = \textcolor{b l u e}{33}$

Nov 7, 2017

$k$ is the actual number;
$n$ is the position of that number in the sequence.

${k}_{5} = {2}^{5} + 1 = 32 + 1 = 33$

#### Explanation:

[Note that I rewrote your question to use ${k}_{n}$ to denote the $n$th value for $k$ in the sequence (and to add some clarity)]

${k}_{5}$ is the $5$th number in the sequence