The sequence (Sₙ) is defined by the recursion formula: Sₙ+1 = n + 1/2n * Sₙ, S₁ = 1. Determine an explicit formula for the nth term Sₙ in the sequence.
a) Sₙ = n²
b) Sₙ = (n+1)/2
c) Sₙ = 2n+1
d) Sₙ = n/2