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

Guest May 17, 2020

#1**0 **

The first term is 1 and each successive term is the sum of all the previous terms:

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

Although not true for the first term, each of the following terms has a value of 2^{n - 2}

where n is the number of the term.

We want 2^{n - 2} >= 5000

log(2^{n - 2}) >= log(5000)

(n - 2)log(2) >= log(5000)

n - 2 >= log(5000)/log(2)

n - 2 >= 12.29

n >= 14.29

So: n = 15

geno3141 May 17, 2020