Lor
2023 AMC 8
Problem 25
Fifteen integers 
are arranged in order on a number line. The integers are equally spaced and have the property that![\[1 \le a_1 \le 10, \thickspace 13 \le a_2 \le 20, \thickspace \text{ and } \thickspace 241 \le a_{15}\le 250.\]](https://latex.artofproblemsolving.com/1/d/2/1d2ca926ca9cbd962c46878abaecad6ef507d5ff.png)
What is the sum of digits of 
We call a1 = a and a2 – a1 = d
So a15 = a+14d
241 <= a+14d <= 250
Consider
a=1
a=2
a=3
Then you will see a=3 works ( after checking some cases you can prove other cases don’t work)
Solution