Algebra II / Mr. Hansen 4/7/2006

Name: _________E period_________ (10 pts.)

Test on Chapter 11: Sequences, Series, Binomial Theorem

Time limit: 26 minutes. A calculator is required.
Each problem is worth 3 points. There is no partial credit. Write the capital letter of the
best choice, or fill in the word or phrase that best fits each blank.

	For problems 1-5, identify each numbered item as one of the following: (A) if it is an arithmetic sequence (B) if it is an arithmetic series (C) if it is a geometric sequence (D) if it is a geometric series (E) if it is something else.
1. ____	555 + 666 + 777 + 888 + 999
2. ____	2/3, 1, 1.5, 2.25
3. ____	2 – 1 + .5 – .25 + .125 – .0625 + . . .
4. ____	0 + 1 + 3 + 7 + 15 + 31 + 63 + . . .
5. ____	5, –5, –15, –25
6. ____	In the phrase “arithmetic sequence,” how is the word “arithmetic” pronounced?
	(A) with stress on the first and third syllables (B) with stress on the second syllable only (C) with stress on the fourth syllable only	(D) with stress on the second and fourth syllables (E) with no stress whatsoever
7. ____	A series converges if and only if
	(A) the terms become fairly small (B) the terms approach zero (C) the sequence of partial sums has a limit	(D) the sequence of partial sums is arithmetic (E) the sequence of partial sums is geometric
8.	Standard notation for a common ratio is r, and standard notation for a common difference is ______ .
9.	An infinite geometric series converges if and only if ________________________ . (Fill in the blank. You may use standard notation to save writing.)
10, 11.	Compute the numeric value for #3 and #4. If the value does not exist as a number, write “DNE.”
	3. Answer: ________________________________
	4. Answer: ________________________________
12. ____	In #3, S3 equals
	(A) .5 (B) 1.5 (C) 2.5	(D) 3.5 (E) none of these
13. ____	Compute the sum of the first 3000 counting numbers (1 through 3000).
	(A) 4,500,000 (B) 4,500,500 (C) 4,501,000	(D) 4,501,500 (E) none of these
14, 15.	“Full work” generally consists of three components: formula (equation), _______________ , and circled result. The circled result should include proper _______________ in word problems.
16-18.	Find the 741st term of this sequence: 55, 44, 33, 22, 11, 0, –11, –22, . . . Show all three components of your proper work.
19-21.	In the series 5 + 2.5 + 1.25 + .625 + .3125 + . . . , at least how many terms must we sum in order to make the partial sum exceed 9.9995? Show a relevant formula (equation or inequality); then either solve or use “brute force” to find the answer.

22. ____	Bridge is a game played with a standard 52-card deck. Each player receives a hand consisting of 13 cards, randomly drawn. How many different bridge hands are possible?
	(A) approximately 6.35 billion (B) approximately 63.5 billion (C) approximately 635 billion	(D) approximately 6.35 trillion (E) approximately 63.5 trillion
23. ____	How many terms are in the expansion of (a + b)^n, where n is a positive integer?
	(A) n – 1 (B) n (C) n + 1	(D) 2ab (E) impossible to determine
24. ____	The 4th term in the expansion of (q + w)^9 equals
	(A) q^6w^6 (B) q^6w^3 (C) 122q^6w^6	(D) 122q^6w^3 (E) none of these
25. ____	The even-numbered terms in the expansion of (q – w)^n all have what general form?
	(A) + q^nw^n (B) – q^nw^n (C) + q^rw^n^– r	(D) – q^rw^n^– r (E) none of these
26. ____	Give a real-world example of a geometric sequence.
	(A) the phase-out schedule of a government program that is being cut to 75%, 50%, 25%, and finally 0% of its original funding (B) the pitches (in cycles per second) of the notes on a grand piano (C) the interest payable at the end of each year that a bond is in effect (simple interest, not compound interest) (D) the side lengths of an isosceles triangle (E) all of the above
27-30.	Write out the first 3 terms of , and then compute the sum. Show all three components of your proper work.