The 13th term of an arithmetic progression is 10 and the 25th term is 20. Calculate: i) the common difference ii) the first term. iii) the 17th term.

Here's how to solve this arithmetic progression problem:

The formula for the $n$-th term of an arithmetic progression is $a_n = a_1 + (n-1)d$, where $a_1$ is the first term and $d$ is the common difference.

Given:
$a_{13} = 10$
$a_{25} = 20$

This gives us two equations:

1. $a_1 + (13-1)d = 10 \Rightarrow a_1 + 12d = 10$
2. $a_1 + (25-1)d = 20 \Rightarrow a_1 + 24d = 20$