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5) The sum of the terms of a sequence is called a(n)

Question : 5) The sum of the terms of a sequence is called a(n) : 2151539

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Fill in the blank with one of the words or phrases listed below.

1) A(n) _____ is a function whose domain is the set of natural numbers {1, 2, 3, . . . , n}, where n is some natural number.

A) series

B) infinite sequence

C) factorial of n

D) finite sequence

2) The _____, written n!, is the product of the first n consecutive natural numbers.

A) series

B) arithmetic sequence

C) factorial of n

D) infinite sequence

3) A(n) _____ is a function whose domain is the set of natural numbers.

A) infinite sequence

B) factorial of n

C) finite sequence

D) series

4) A(n) _____ is a sequence in which each term (after the first) is obtained by multiplying the preceeding term by a constant amount r. The constant r is called the _____ of the sequence

A) arithmetic sequence, common difference

B) geometric sequence, common difference

C) arithmetic sequence, common ratio

D) geometric sequence, common ratio

5) The sum of the terms of a sequence is called a(n) _____.

A) series

B) general term

C) infinite sequence

D) finite sequence

6) The nth term of a sequence an is called the _____.

A) common ratio

B) general term

C) factorial of n

D) common difference

7) A(n) _____ is a sequence in which each term (after the first) differs from the preceeding term by a constant amount d. The constant d is called the _____ of the sequence

A) arithmetic sequence, common difference

B) geometric sequence, common ratio

C) arithmetic sequence, common ratio

D) geometric sequence, common difference

8) A triangular array of the coefficients of the terms of the expansion of (a + b)n is called _____ .

A) Pascal's triangle

B) series

C) infinite sequence

D) factorial of n

Find the indicated term(s) of the given sequence.

9) The first five terms of the sequence an = ((-1)n/n2 - 3)

A) - (1/3), (1/2), 1, - (1/6), (1/13)

B) (1/2), 1, - (1/6), (1/13), (1/22)

C) - (1/2), - 1, (1/6), - (1/13), (1/22)

D) (1/2), 1, - (1/6), (1/13), - (1/22)

10) The eighth term of the sequence an = 7 - 2(n - 1)

A) -9

B) 23

C) 21

D) -7

11) The general term of the sequence 3, (3/2), (3/4), (3/8), (3/16), . . .

A) an = 3 ((1/2))n + 1

B) an = 3 ((1/4))n - 1

C) an = 3 ((1/2))n

D) an = 3 ((1/2))n - 1

12) The general term of the sequence -3, 9, -27, 81, . . .

A) an = 3n

B) an = (-1)n+1 3n+1

C) an = 3n+1

D) an = (-1)n 3n

Find the partial sum of the given sequence.

13) S5 of the sequence an = 3(4)n - 1

A) 63

B) 323

C) 341

D) 1023

14) S20 of the sequence an = -1 + 7(n - 1)

A) 1380

B) 1310

C) 1245

D) 1035

15) S of the sequence a1 = 13, r = (1/3)

A) (13/4)

B) (39/4)

C) (13/2)

D) (39/2)

16) S of the sequence 4, - (4/3), (4/9), . . .

A) 3

B) 4

C) (8/3)

D) - (4/3)

17)

A) 3

B) -10

C) -16

D) -20

18)

A) 366

B) -270

C) 378

D) 702

Expand the binomial.

19) (p - q)6

A) p6 - 8p5q + 17p4q2 - 22p3q3 + 17p2q4 - 8pq5 + q6

B) p6 - q6

C) p6 - 6p5q - 30p4q2 + 120p3q3 + 360p2q4 - 720pq5 - 720q6

D) p6 - 6p5q + 15p4q2 - 20p3q3 + 15p2q4 - 6pq5 + q6

20) (5x - 2y)3

A) 25x3y - 20x2y2 + 4xy3

B) 125x3 - 50x2y + 20xy2 - 8y3

C) 25x3y - 10x2y2 + 4xy3

D) 125x3 - 150x2y + 60xy2 - 8y3

Solve the problem.

21) The population of a small town is growing yearly according to the sequence defined by an = 450 + 55(n - 1), where n is the number of the year just beginning. Predict the population at the beginning of the eighth year. Find the town's initial population.

A) 835 people; 505 people initially

B) 835 people; 450 people initially

C) 890 people; 505 people initially

D) 890 people; 450 people initially

22) A stocker at a grocery store has created a display of stacked cans such that the top row contains 2 cans, the second row contains 4 cans, the third row contains 6 cans, and so on for six rows. Write the finite series of this sequence, and find the total number of cans in the display.

A) 2 + 4 + 6 + 8 + 10 + 12; 32 cans

B) 4 + 6 + 8 + 10 + 12 + 14; 54 cans

C) 4 + 6 + 8 + 10 + 12 + 14; 44 cans

D) 2 + 4 + 6 + 8 + 10 + 12; 42 cans

23) A pendulum swings through an arc of length 90 inches on its first swing. On each successive swing, the length of the arc is (5/6) the length of the arc on the preceding swing. Find the length of the arc on the fourth swing, and find the total arc length for the first four swings. Round to two decimal places.

A) 52.08 in.; 279.58 in.

B) 52.08 in.; 227.50 in.

C) 43.40 in.; 227.50 in.

D) 43.40 in.; 279.58 in.

24) A pendulum swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only (3/5) as far as on the previous swing. How far will it swing altogether before coming to a complete stop? If necessary, round to the nearest inch.

A) 267 in.

B) 133 in.

C) 100 in.

D) 200 in.

25) A gambler has a specific betting system where the first bet made is $10, the second bet made is $20, the third bet is $40, and so on. Find how much the gambler bets on the seventh bet. Find the total amount of money the gambler has bet over the first seven bets.

A) $120; 570

B) $140; 430

C) $140; 570

D) $120; 430

26) Use the formula S to write 0.49overbar(49) as a fraction.

A) (49/1000)

B) (49/99)

C) (4900/99)

D) (49/100)

Solution
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