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Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 20 and 2500, respectively. (5 points)

Let u = , v = . Find -3u + 5v. (5 points)

Find the center, vertices, and foci of the ellipse with equation 4×2 + 9y2 = 36. (5 points)

Find the limit of the function by using direct substitution. (6 points)  

Find the first six terms of the sequence. a1 = -2, an = 3 • an-1 (5 points)

Use graphs and tables to find the limit and identify any vertical asymptotes of the function. (5 points)

(04.03 MC)  A person has a 30 percent chance of winning on a scratch-off lottery ticket. What is the probability she first wins of the fifth ticket? (4 points)

Find the limit of the function algebraically. (5 points)  

Find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at y = ± x. (5 points)

Predict whether the following reaction will occur spontaneously or non-spontaneously. Give detailed reasons for your selection.                        2S(s)   +  3O2 (g)       →        2SO3 (g)     +    21Kcal