We are given an arithmetic sequence $\{a_n\}$. The sum of the first $n$ terms is denoted by $S_n$. We are given that $a_6 = 16$ and $S_5 = 35$. We need to find the common difference $d$ of the arithmetic sequence.

1. Problem Description

We are given an arithmetic sequence $\{a_n\}$. The sum of the first $n$ terms is denoted by $S_n$. We are given that $a_6 = 16$ and $S_5 = 35$. We need to find the common difference $d$ of the arithmetic sequence.

2. Solution Steps

We have the following formulas for arithmetic sequences:

$a_n = a_1 + (n-1)d$

$S_n = \frac{n}{2}(2a_1 + (n-1)d)$

Using the given information, we have:

$a_6 = a_1 + 5d = 16$ (1)

$S_5 = \frac{5}{2}(2a_1 + 4d) = 35$ (2)

Simplifying equation (2):

$5(2a_1 + 4d) = 70$

$2a_1 + 4d = 14$

$a_1 + 2d = 7$ (3)

Now we have a system of two equations with two unknowns $a_1$ and $d$:

$a_1 + 5d = 16$ (1)

$a_1 + 2d = 7$ (3)

Subtracting equation (3) from equation (1):

$(a_1 + 5d) - (a_1 + 2d) = 16 - 7$

$3d = 9$

$d = 3$

3. Final Answer

The common difference $d = 3$.

The answer is A.