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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?

 Apr 16, 2021
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The  terms  are

 

1,  2,  4,  8, 16, 32........

 

The  nth  term appears to be 2^(n-1)

 

So....we  need  to solve  this

 

2^(n - 1)  = 5000      take  the log of  both sides

 

log 2^(n - 1)  = log 5000    and we  can write

 

(n - 1)  log2  =  log 5000

 

n - 1  = log 5000 / log 2

 

n = log 5000 / log 2  +  1  ≈ 13.28

 

So....the  14th  term will exceed 5000

 

 

cool cool cool

 Apr 16, 2021

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