Find the explicit formula for the following sequence 4,8,16,32,...

Question

Layton Leach · Accepted Answer

I am not sure of the use of the word explicit, but perhaps this will help.
4, 8, 16, 32 are all powers of 2, but the sequence does not start from the first power of 2 which would be 2.
n tells us the position in the sequence of a particular term.
n always starts from 1 for the first term, 2 for the second and so on.. Try to find a pattern or rule which links n to the value of the corresponding term.
We would like to have

2^{1} = 2

,

2^{2} = 4

,

2^{3} = 8

as the first three terms, because then the index n matches the position in the sequence.
However in the sequence we are working with, the first term is 4, which is 2², with the index being 1 more than n.
The terms can then be given as

2^{n + 1}

The general term would be

T_{n} = 2^{n + 1}

Find the explicit formula for the following sequence 4,8,16,32,...

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