Exam 12: Sequences, Series, and Probability

Solve the problem. -A pendulum swings through an arc of 160 centimeters. On each successive swing, the length of the arc ise length of the arc is $\frac { 2 } { 3 }$ of o the length of the previous length. Find the total distance the pendulum travels before it comes to rest.

Use the binomial theorem to expand the expression. - $( x + 5 ) ^ { 4 }$

Solve the problem. -A marble is taken out of a bag containing 115 marbles: 25 red, 35 blue, 15 green, and 40 orange. Find the probability: P(a red and a blue marble is chosen)

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence. -15, 6, -3, -12, . . ., -156

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the arithmetic sequence. - $a = 2 , d = 7 ; \text { find } a _ { n } \text { and } a_{ 16}$

Find the first and third partial sums, s1 and s3, for the sequence - $a _ { n } = 3 n + 9$

Solve the problem. -Doctors predict that by administering a vaccine, the number of new cases of a certain disease will decrease by half each year. If 1200 people were afflicted with the disease in 2000, estimate the number of new cases in 2005. (Round to the nearest whole number, if necessary.)

Solve the problem. -A spinner is spun. Assuming that the spinner cannot land on a line, find the probability of landing on a color that is not blue.