Solve for a_2
a_{2}=d+a_{n}-dn
Solve for a_n
a_{n}=dn+a_{2}-d
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a_{n}=a_{2}+nd-d
Use the distributive property to multiply n-1 by d.
a_{2}+nd-d=a_{n}
Swap sides so that all variable terms are on the left hand side.
a_{2}-d=a_{n}-nd
Subtract nd from both sides.
a_{2}=a_{n}-nd+d
Add d to both sides.
a_{n}=a_{2}+nd-d
Use the distributive property to multiply n-1 by d.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}