The 3rd term $(a_3)$ of an Arithmetic Progression is 10, and the 7th term $(a_7)$ is 22.

Use the formula $d = \frac{a_7 - a_3}{7 - 3}$. Simply calculate the difference between terms and divide by the difference in their positions.

Students often miscalculate the difference in positions $(7-3)$ as 3 instead of 4, or confuse the term formula $a_n = a + (n-1)d$ by forgetting the $(n-1)$ part.

This logic is identical to finding the slope of a linear function $y = mx + c$, where the common difference $d$ acts as the slope $m$ between two points $(n, a_n)$.