Basic Math Examples

$A = a + (n - 1) d$

Step 1

Rewrite the equation as $a + (n - 1) d = A$ .

$a + (n - 1) d = A$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$a + n d - 1 d = A$

Step 2.2

Rewrite $- 1 d$ as $- d$ .

$a + n d - d = A$

Step 3

Subtract $a$ from both sides of the equation.

$n d - d = A - a$

Step 4

Factor $d$ out of $n d - d$ .

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Step 4.1

Factor $d$ out of $n d$ .

$d n - d = A - a$

Step 4.2

Factor $d$ out of $- d$ .

$d n + d \cdot - 1 = A - a$

Step 4.3

Factor $d$ out of $d n + d \cdot - 1$ .

$d (n - 1) = A - a$

Step 5

Divide each term in $d (n - 1) = A - a$ by $n - 1$ and simplify.

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Step 5.1

Divide each term in $d (n - 1) = A - a$ by $n - 1$ .

$\frac{d (n - 1)}{n - 1} = \frac{A}{n - 1} + \frac{- a}{n - 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $n - 1$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{d (n - 1)}{n - 1} = \frac{A}{n - 1} + \frac{- a}{n - 1}$

Step 5.2.1.2

Divide $d$ by $1$ .

$d = \frac{A}{n - 1} + \frac{- a}{n - 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$d = \frac{A}{n - 1} - \frac{a}{n - 1}$

Step 5.3.2

Combine the numerators over the common denominator.

$d = \frac{A - a}{n - 1}$