please help

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