We are given an arithmetic sequence $\{a_n\}$ with common difference $d = \frac{1}{2}$ and $a_{17} = 10$. We need to find the sum of the first 17 terms, $S_{17}$.

1. Problem Description

We are given an arithmetic sequence $\{a_n\}$ with common difference $d = \frac{1}{2}$ and $a_{17} = 10$. We need to find the sum of the first 17 terms, $S_{17}$.

2. Solution Steps

The general formula for the $n$-th term of an arithmetic sequence is:

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

We are given $a_{17} = 10$ and $d = \frac{1}{2}$. We can use the formula to find $a_1$:

$a_{17} = a_1 + (17-1)d$

$10 = a_1 + 16 \cdot \frac{1}{2}$

$10 = a_1 + 8$

$a_1 = 10 - 8 = 2$

The formula for the sum of the first $n$ terms of an arithmetic sequence is:

$S_n = \frac{n}{2}(a_1 + a_n)$

We want to find $S_{17}$, so we have:

$S_{17} = \frac{17}{2}(a_1 + a_{17})$

$S_{17} = \frac{17}{2}(2 + 10)$

$S_{17} = \frac{17}{2}(12)$

$S_{17} = 17 \cdot 6$

$S_{17} = 102$

3. Final Answer

The sum of the first 17 terms is

1

0

2. So the answer is (D).