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

##### 2 Answers

The 5th number in the sequence is

#33# .

#### Explanation:

In this problem,

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

When

#k = 2^color(red)1+1 = 2+1 = color(blue)3#

When

#k = 2^color(red)2+1 = 4+1 = color(blue)5#

When

#k = 2^color(red)3+1 = 8+1 = color(blue)9#

When

#k = 2^color(red)4+1 = 16+1 = color(blue)17#

This is the sequence that the problem gives us:

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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We can do this by plugging in

#k = 2^color(red)5 + 1 = 32 + 1 = color(blue)33#

*Final Answer*

#### Explanation:

[Note that I rewrote your question to use