To evaluate the arithmetic series given, we can use the formula for the sum of an arithmetic series:

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

where:

• $a_1 = 17$ (the first term),
• $a_n = 143$ (the last term),
• $n = 15$ (the number of terms).

Step-by-Step Solution:

1. Substitute the values into the formula:

   $S_{15} = \frac{15}{2} \cdot (17 + 143)$

2. Calculate the sum inside the parentheses:

   $17 + 143 = 160$

3. Now, substitute back to get:

   $S_{15} = \frac{15}{2} \cdot 160$

4. Simplify the multiplication:

   $S_{15} = 15 \cdot 80 = 1200$

Answer:

The correct answer is 1200.

Would you like a more detailed explanation, or do you have any questions?

Here are five related questions to consider:

1. How would the sum change if $n$ were increased to 20?
2. What is the common difference in this series?
3. How can we derive the formula for the sum of an arithmetic series?
4. What would the sum be if the first term changed to 10?
5. How do we determine the common difference when only given the first and last terms and the number of terms?

Tip: In an arithmetic series, the common difference can be found by dividing the difference between the last and first term by the number of terms minus one.