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?
+129849 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
