Exam 9: Sequences, Series, and Probability

Write the first five terms of the sequence defined recursively. Use the pattern to write the nth term of the sequence as a function of n. (Assume that n begins with 1.)

The probability that a basketball player will make a given free throw is . To find the probability that the player makes exactly 8 out of her next 10 free throws, evaluate the term in the expansion of . Round to four decimal places.

Use the binomial theorem to expand the binomial.

Find the sum of the infinite series.

Several logs are stored in a pile with 22 logs on the bottom layer, 21 on the second layer, 20 on the third layer, and so on. If the top layer has one log, how many logs are in the pile?

Evaluate the sum.

Evaluate the expression.

Calculate the binomial coefficient:

Find the sum of the infinite geometric sequence. 3 - 0.75 + 0.1875 ...

Several logs are stored in a pile with 18 logs on the bottom layer, 17 on the second layer, 16 on the third layer, and so on. If the top layer has one log, how many logs are in the pile?

Find the sum of the indicated terms of the geometric sequence. 2, 4, 8 ... (to 8 terms)

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) 1, 6, 11, 16, 21

Use summation notation to write the sum.

Evaluate the expression. P (6, 6)

Match the arithmetic sequence with its graph from the choices below.

Determine whether the sequence is arithmetic. If so, find the common difference. 5, 25, 125, 625, 3125

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) 5, 8, 11, 14, 17

Find the sum using the formulas for the sums of powers of integers.

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.) 9, 12, 15, 18, 21