5. A geometric sequence has a third term of 20 and seventh term of 324/125. Find the two possible common ratios, and the initial term.

5: Determine whether the alternating series converges. \sum_{n=1}^{\infty}(-1)^{n+1} \frac{1}{n^{2}}

Let a, a, a3,..., an.... be a geometric sequence with common ratio r. Find S5. a₁ = 3, a5 = 768, r=4

A woman borrows $4000 at 9% compounded monthly, which is to be amortized over 3 years in equal monthly payments. For tax purposes, she needs to know the amount of interest paid during each year of the loan. Find the interest paid during the first year, the second year, and the third year of the loan. [Hint: Find the unpaid balance after 12 payments and after 24 payments.]C

A person purchased a $146,567 home 10 years ago by paying 10% down and signing a 30-year mortgage at 9% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20-year mortgage at 4.5% compounded monthly. How much interest will refinancing save?

3. [3 marks] Determine whether each of the following functions from Z to Z is one-to-one. If it is not, then justify. \begin{array}{l} \text { (a) } f(n)=n-10 \\ \text { (b) } f(n)=n^{2}+3 \\ \text { (c) } f(n)=16\left[\frac{n}{7}\right\rfloor \end{array}

\text { Sketch the curve defined by the parametric equations } x=\sqrt{t+3} \text { and } y=t+3 \text {. }

\text { In a geometric sequence } u_{1}=125 \text { and } u_{6}=\frac{1}{25} (a) Find the value of r (the common ratio) (b) Find the largest value of n for which S. <156.22 (c) Explain why there is no value of n for which S, >160

A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation C(x)where C(x) is the cost in dollars for handling x cases per month. The average cost per case is given by C(x)=-X Complete parts (A) through (C).

\text { 6. (8 points) Test the convergence of the series } \sum_{n=1}^{\infty} n e^{-2 n} \text { by applying } a.The ratio test. b. The integral test.