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

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Answer 1 · 2016-11-19T10:08:27

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

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: $a_n = 2^(2n-1)$

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