Exam 13: Sequences and Series

Find the sum of the series , for .

Is a geometric series?

The following table shows the enrollment in a private college for the years 1996 to 2005. Interpret these figures as partial sums, , of terms of a sequence, , where n is the number of years since 1995 (so , etc.). Which of the following gives the total enrollment in 2004?

If denotes your total earnings after n weeks of work, what is the average amount of money you earned each week for the first 8 weeks?

What is ?

Your doctor tells you to take 38 mg of a certain drug every 12 hours. It is known that only 6% of the drug is still in the body at the end of 12 hours. Assuming you continue to take the drug, what happens to the drug level in the long run? Give your answer correct to 3 decimal places.

What is the 8^th term of the sequence 1, 0.3, -0.4, -1.1, -1.8, . . .? The sequence is either arithmetic or geometric.

Let be an arithmetic sequence with and . What is ?

Is the series arithmetic, geometric, or neither?

A sequence can be defined by a recurrence relation, which gives the first term, , and a formula for finding in terms of the previous term, . For the recurrence relation below, what is ?

If you were to fill out a pedigree chart, the first column would have one name (yours), the second column would have two names (your parents), the third column would have 4 names (your grandparents), etc. How many names would be on the chart if there were 13 columns total?

For what values of x does the sum converge?

What is the 9^th term of the sequence 1, 3, 9, 27, 81, . . .? The sequence is either arithmetic or geometric.

Let , with . As , what happens to S?

Find the sum of the first 200 odd integers.

What is the sum of the first 18 positive even integers?

The time it takes an employee to assemble a bicycle is 56 minutes the first time he does it. The second time, it take him 55 minutes; the third time it takes 54 minutes, and so on. If this trend continues, how many minutes will it take him to assemble the 15^th bicycle?

Does ?

Is the sequence arithmetic, geometric, neither, or both?

Find the sum of the series .