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The first term of a given sequence is 1, and each successive term is the sum of all the previous terms of the sequence, plus 1. What is the value of the first term which exceeds 5000?

 Oct 20, 2021
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Your sequence is:

 

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, ...etc.

 

The "closed form" of the sequence is:

 

a(n) =2^(n - 1)

 

2^(n - 1) > 5000, solve for n

 

n>=14   and  2^(14 - 1 )==2^13 =8,192 - the value of the 14th term.

 Oct 20, 2021

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