Exam 9: Sequences, Series, and Probability

Find the sum:

Find the sum of the finite geometric series 1 + 2 + 4 + 8 + ... + 64.

Find the coefficient, C, of the term in the binomial expansion.

Expand using Pascal's Triangle.

Find the common difference d of the arithmetic series 74, 70, 66, 62, 58, ...

Find the sum of the infinite geometric series . Round the answer to 3 decimal places if necessary.

An outdoor amphitheater has 90 seats in the front row and each subsequent row has 2 more seats than the previous row. How many seats are in in the amphitheater if there are 38 rows?

Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1.

Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1.

In a deck of 52 cards, how many different 3-card hands can be dealt?

Expand the expression using the binomial theorem.

Find the probability of tossing 7 coin a times and getting exactly 6 tails.

Expand using the binomial theorem.

Simplify the ratio of factorials .

Evaluate the binomial coefficient .

Find the common difference d of the arithmetic series 5, 7, 9, 11, 13, ...

At Point Loma Soup and Salad restaurant, there are 4 types of lettuce, 8 types of salad ingredients, and 5 different dressings to choose from. How many different salads can be made from one type of lettuce, one salad ingredient, and one dressing?

Evaluate the binomial coefficient .

Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1.

In a particular state there are seven characters in a license plate: three letter(s) followed by four numbers. If 0s and 1s are eliminated from possible numbers and Os and Is are eliminated from possible letters, how many different license plates can be made?