Exam 15: Sequences, Series, and the Binomial Theorem

Solve the problem. -A pendulum swings through an arc of 660 centimeters. On each successive swing, the length of the arc is of the length of the previous length. Find the total distance the pendulum travels before it comes to rest.

Find the indicated quantity of the arithmetic sequence. -

Find the indicated term of the sequence whose nth term is shown. -

Write the expression for the general (or nth) term, an, of the geometric sequence. -

Find the sum of the infinite geometric series. -

Write the first three terms of the expansion. -

Find the indicated term of the sequence whose nth term is shown. -

Find the arithmetic mean of the following set of data. -4, 16, 64, 256, 1024

Find the indicated sum. -

Find the sum, of the sequence. --1, -5, -9, -13, . . ., -77

Write the first five terms of the sequence whose nth term is shown. -an = 4n - 1

Write the expression for the general (or nth) term, an, of the arithmetic sequence. -

Find the first and third partial sums, s1 and s3, for the sequence -

Solve the problem. -A grocery store display of apples has a total of 16 rows. The bottom row requires 104 apples. Each successive row requires 5 less apples than the prior one. How many apples are required to build the display?

Evaluate the combination. -

Write the first five terms of the sequence whose nth term is shown. -

Write the next three terms of the sequence. -4, 16, 64, 256, . . .

For the geometric sequence, find the common ratio, r. -3, 9, 27, 81, 243, . . .

Evaluate the series. -

Use the binomial theorem to expand the expression. -