To find the limit of the sequence an, we need to analyze the behavior of the sequence as n approaches infinity. Let's break down the steps to calculate the limit.

Step 1: Write out the terms of the sequence to observe a pattern.

Given: a1 = a, a2 = b, and an = (a + an-1)/2 for n ≥ 2.

The terms of the sequence are:
a1 = a
a2 = b
a3 = (a + b)/2
a4 = (a + (a + b)/2)/2
a5 = (a + (a + (a + b)/2)/2)/2

We can see a pattern emerging as we calculate more terms.

Step 2: Observe the pattern and make a conjecture.

Looking at the terms of the sequence, we can see that each term is calculated by taking the average of the previous term and a constant value. In this case, the constant value is a.

We can conjecture that as n approaches infinity, the terms of the sequence will approach the average of the previous term and the constant value a.

Step 3: Prove the conjecture.

To prove the conjecture, we can use mathematical induction.

Base case: For n = 2, we have a2 = b. This is consistent with the conjecture.

Inductive step: Assume that the conjecture holds for some n = k, i.e., ak = (a + ak-1)/2. We need to show that it also holds for n = k + 1, i.e., ak+1 = (a + ak)/2.

Using the assumption, we can substitute ak-1 = (a + ak)/2 into the expression for ak+1 to get:
ak+1 = (a + (a + ak)/2)/2
= (2a + a + ak)/4
= (a + ak)/2

This proves that the conjecture holds for n = k + 1.

Step 4: Calculate the limit.

Since the conjecture holds for all n, as n approaches infinity, the terms of the sequence will approach the average of the previous term and the constant value a.

Therefore, the limit of the sequence an is (a + b)/2.

Hence, the correct answer is option 'C' - (a + b)/2.