Answer
\[n=\frac{{{a}_{n}}-{{a}_{1}}}{d}+1\]
Work Step by Step
The given equation is:
\[{{a}_{n}}={{a}_{1}}+\left( n-1 \right)d\]
Simplify the given equation for n:
Subtract a1 from both sides, followed by dividing both sides by d, then finally add 1 to both sides.
\[\begin{align}
& \left( n-1 \right)d={{a}_{n}}-{{a}_{1}} \\
& n-1=\frac{{{a}_{n}}-{{a}_{1}}}{d} \\
& n=\frac{{{a}_{n}}-{{a}_{1}}}{d}+1 \\
\end{align}\]
This formula is for nth term of an arithmetic sequence, whose first term is a1 and
common difference is d.
