Recall that an increasing sequence $a_1\lt a_2\lt a_3\lt \dots\lt a_t)$ of integers is called an arithmetic progression when there exists a positive integer $d$ for which $a_{i+1}-a_i=d\text{,}$ for all $i=1,2,\dots,t-1\text{.}$ The integer $t$ is called the length of the arithmetic progression.