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
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= color(red)1#:

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

When #n= color(red)2#:

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

When #n= color(red)3#:

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

When #n= color(red)4#:

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

This is the sequence that the problem gives us: #color(blue)3, color(blue)5, color(blue)9, color(blue)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=color(red)5#, so that #k# will be the #5#th term in the sequence.

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

Final Answer

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