## Thinking Mathematically (6th Edition)

$d=\frac{{{a}_{n}}-{{a}_{1}}}{n-1}$
The given equation is: ${{a}_{n}}={{a}_{1}}+\left( n-1 \right)d$ Simplify the given equation for d: Subtract a1 from both sides, then divide both sides by (n-1) \begin{align} & \left( n-1 \right)d={{a}_{n}}-{{a}_{1}} \\ & d=\frac{{{a}_{n}}-{{a}_{1}}}{n-1} \end{align} This formula is for nth term of an arithmetic sequence, whose first term is a1 and Common difference is d.