The Mathmetics of Principal & Sequence

Core Reading Material: Sections 11.3, 11.4, and 11.5

Point Value: 20 points in all (3 points per question, except as noted)

Directions: Solve the 7 problems listed below on your own, with the assistance of your book and classroom notes. Submit your answers HERE through Blackboard. You may either use the text editor provided to enter the answers directly, or you may attach a file (or files) that contain your work. For example, you can put your answers in an MS Word file and submit that, or you could take pictures of handwritten work and submit the picture files to me as attachments.Where appropriate, you should always provide some supporting work to explain how you arrived at a given answer. Correct answers without any supporting explanation may not receive 100% credit.

Problems to Solve:

[Note: Unless specified differently, round monetary answers to the nearest penny.]

(1) [2 pts] A “fibonacci type” sequence has s1 = 6 and s2 = 3. List the first five terms of the sequence. Then find S5, the sum of the first five terms.

(2) For the arithmetic sequence whose first four terms are 5, 7, 9, 11, … . Find A88, the sum of the first 88 terms of the sequence.

(3) Find the value of the summation:

(4) Find the value of the sum: 6 + 13 + 20 + 27 + … + 398 + 405 + 412 + 419

(5) A geometric sequence has a first term of g1 = 10 and a common ratio of r = -2. Find G9, the sum of the first 9 terms of the sequence, in two ways. Write out the terms and find the sum “by hand” and also find it using the formula:

(6) Suppose that you deposit $50 at the end of every month into an account that gives 6% annual interest, compounded monthly. You do this over a period of 8 years. How much will you have in your account at the end of the 8 year period ?
(7) At the end of every quarter over the course of 5 years, a person deposits $400 into an investment account. The account the money is deposited into gives 5% annual interest, compounded quarterly. Conisdering the fact that the person will ultimately deposit $8,000 of their own money into the account, how much interest will the person have made at the end of the 5 years ?.