Exam 10: Sequences, Series and Probability

Find the total length of the red-line curve in the figure if the width of the maze formed by the curve is 32 inches and all halls in the maze have width 2 inches. in. and in.

Evaluate the expression.

A committee is going to select 28 students from a pool of 800 to receive scholarships. How may ways could the students be selected if each scholarship is worth the same amount?

Find the sum of the arithmetic sequence that satisfies the stated conditions.

Use the principle of mathematical induction to find the factor of the expression. Hint:

Express the sum in terms of n. (Hint: Use the theorem on sums to write the sum as . Next, use the following formulas and the theorem on the sum of a constant.)

A company is to distribute $28,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $4,400, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

Find the number.

Use the binomial theorem to expand and simplify.

During 1990, smoking caused 418,890 deaths in the United States. Of these deaths, cardiovascular disease accounted for 179,820, cancer for 151,322, and respiratory diseases such as emphysema for 84,475. Find the probability that a smoking-related death was the result of either cardiovascular disease or cancer.

In a round-robin tennis tournament, every player meets every other player exactly once. How many players can participate in a tournament of 78 matches?

A contest will have five cash prizes totaling $6,000, and there will be a $100 difference between successive prizes. Find the first prize.

Bode's sequence, defined by can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.

Find the nth term and the fifth term of the geometric sequence.

Use the principle of mathematical induction to find the equivalent expression for every positive integer n.

Find the specified term of the arithmetic sequence that has the two given terms.

Find the third term of the geometric sequence whose first two terms are 3 and 9.

Evaluate the expression.

Without expanding completely, find the term in the expansion of the expression that contains .

Find the number of terms in the arithmetic sequence with the given conditions. ,