Solve f(n)-f(n-1)=15text{and}f(1)=4W

$$f ( n ) - f ( n - 1 ) = 15 \text { and } f ( 1 ) = 4 W$$

Solve for f, n, W

$$f=15$$

$$n\in \mathrm{R}$$

$$W = \frac{15}{4} = 3\frac{3}{4} = 3.75$$

Solution Steps

Consider the first equation. Use the distributive property to multiply f by n-1.

$$fn-\left(fn-f\right)=15$$

To find the opposite of fn-f, find the opposite of each term.

$$fn-fn+f=15$$

Combine fn and -fn to get 0.

$$f=15$$

Consider the second equation. Insert the known values of variables into the equation.

$$15\times 1=4W$$

Multiply 15 and 1 to get 15.

$$15=4W$$

Swap sides so that all variable terms are on the left hand side.

$$4W=15$$

Divide both sides by 4.

$$W=\frac{15}{4}$$

The system is now solved.

$$f=15 W=\frac{15}{4}$$