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How do you find nth term rule for #2,8,32,128,...#?

1 Answer

Nov 19, 2016

#a_n = 2^(2n-1)#

Explanation:

Consider the given sequence: 2, 8, 32, 128, ...

Notice that each term is an odd power of 2:

#a_1 = 2 = 2^1#
#a_2 = 8 = 2^3#
#a_3 = 32 = 2^5#
#a_4 = 128 = 2^7#

In general the sequence of the odd naturals is generated by: #i = (2n-1) forall n in NN#

Hence our general term is: #a_n = 2^(2n-1)#

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