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.)

Find the eighth term of the geometric sequence whose second and fourth terms are 4 and 16.

Calculate the binomial coefficient:

Use the binomial theorem to expand the binomial.

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

Find the sum of the indicated terms of the geometric sequence. 5, 20, 80 ... (to 5 terms)

Find the eighth term of the geometric sequence whose second and fourth terms are -8 and -32.

The probability that a basketball player will make a given free throw is . To find the probability that the player makes exactly 9 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 indicated partial sum of the series. third partial sum

Determine whether the sequence is arithmetic. If so, find the common difference. 8, 13, 18, 23, 28

Use the binomial theorem to expand the binomial.

Write the first six terms of the arithmetic sequence with the given properties. a = 3, d = 2

Use the Binomial Theorem to expand and simplify the expression.

Determine whether the sequence is geometric. If so, find the common ratio. 3, -1, -5, -9,...

Evaluate using a graphing utility:

Write the first six terms of the sequence defined by the function. f(n) = 6n(n - 1)

Find the indicated nth term of the geometric sequence. 5th term:

Write the first six terms of the arithmetic sequence with the given properties. a = 5, d = 2