A company buys a fleet of six vans for 20,000. During the next 5 years, the fleet will depreciate at a rate of 30 percent per year. (That is, at the end of each year, the depreciated value will be 70percent the value at the beginning of the year.)

(a) Find the formula for the nth term of a geometric sequence that gives the value of the fleet t full years after it was purchased.

(b) Find the depreciated value of the fleet at the end of 5 full years.

Solve for n. $5 \cdot_{n-1} P_{1}=_{n} P_{2}$

A deposit of 50 is made at the beginning of each month in an account that pays 8% interest. compounded monthly. The balance A in the account at the end of 5 years is given by

$A=50\left(1+\frac{0.08}{12}\right)^{1}+\cdots+50\left(1+\frac{0.08}{12}\right)^{00}$. Find A.

Prove the identity. $_{n} C_{n}=_{n} C_{0}$

Find the sum of the infinite geometric series, if possible. If not possible, explain why. $\sum_{k=1}^{\infty} 1.3\left(\frac{1}{10}\right)^{k-1}$

A deposit of P dollars is made at the beginning of each month in an account earning an annual interest rate r, compounded monthly. The balance A after t years is given by $A=P\left(1+\frac{r}{12}\right)+P\left(1+\frac{r}{12}\right)^{2}+\cdots +P\left(1+\frac{r}{12}\right)^{12 t}$ Show that the balance is given by $A=P\left[\left(1+\frac{r}{12}\right)^{12 t}-1\right]\left(1+\frac{12}{r}\right)$

Solve for n. $4 \cdot_{n+1} P_{2}=_{n+2} P_{3}$

In given exercise, find the sum.

$$\sum_{i=0}^4 i^2$$

Use a graphing utility to graph the first 10 terms of the sequence (Assume n begins with 1.) for $a_{n}=-8(0.5)^{n-1}$

In given exercise, find the sum.

$$\sum_{k=1}^5 6$$

Find the sum of the infinite geometric series, if possible. If not possible, explain why. $\sum_{k=1}^{\infty} 4\left(\frac{3}{2}\right)^{k-1}$

Find the sum of the infinite geometric series, if possible. If not possible, explain why. $\sum_{i=1}^{\infty} 6\left(\frac{1}{3}\right)^{i-1}$

Write the first five terms of the sequence. (Assume n begins with 1.) $a_{n}=\frac{n}{n+1}$

Use the Binomial Theorem to expand the complex number. Simplify your result. (Remember that $i=\sqrt{-1}$.) $(2-3 i)^{6}$