Answer
\[d=\frac{{{a}_{n}}-{{a}_{1}}}{n-1}\]
Work Step by Step
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.
