8.1
8.2
8.3
8.5
100
What are the first five terms of the sequence?
an=2n+5
7, 9, 11, 13, 15
100
The nth term of an arithmetic sequence has the equation ______.
an=a1+(n-1)d
100
A sequence is called a _____ sequence if the ratios of consecutive terms are the same. This ratio is called the ______ ratio.
geometric, common
100
A customer can choose one of four amplifiers, one of six compact disc players, and one of five speaker models for an entertainment system. Determine the number of possible system configurations.
Amps: 4, Disc players: 6, Speakers: 5
Total: 4*5*6 = 120 ways
200
Which best describes an infinite sequence? a finite sequence?
(a) the domain consists of the first n positive integers.
(b) the domain consists of the set of positive integers.
Infinite sequence: B
Finite sequence: A
200
Determine whether or not the sequence is arithmetic. If so, find the common difference.
10, 8, 6, 4, 2,...
Arithmetic sequence, d=-2
200
Determine whether or not the sequence is geometric. If so, find the common ratio.
5, 15, 45, 135,...
Geometric sequence, r =3
200
In how many ways can a 10-question true-false exam be answered?
210= 1,024 ways
300
Find the indicated term of the sequence.
an= n2 / (n2+1)
a10= ?
a10= 100/101
300
Write the first 5 terms of the sequence. Then, determine whether or not the sequence is arithmetic. If so, find the difference.
an=8+13n
21, 34, 47, 60, 73
Arithmetic sequence, d=13
300
Write the first five terms of the geometric sequence.
a1= 6, r=3
6, 18, 54, 162, 486
300
How many three-digit numbers can be formed under each condition?
(a) The first digit cannot be zero
(b) The first digit cannot be zero and no repetition of digits is allowed.
(c) The leading digit cannot be zero and the number must be a multiple of 5.
(a) 9*10*10=900 numbers
(b) 9*9*8=648 numbers
(c) 9*10*2=180 numbers
400
Write an expression for the apparent nth term of the sequence. (Assume n begins with 1.)
1,4,7,10,13,...
an=1+(n-1)3
an=3n-2
400
Find the sum of the finite arithmetic sequence.
2+4+6+8+10+12+14+16+18+20
S10=(10/2)(2+20)
=110
400
Write the first five terms of the geometric sequence. Find the common ration and write the nth term of the sequence as a function of n.
a1=9, ak+1=2ak
9, 18, 36, 72, 144
r=2, an=9(2n-1)
400
Find the number of distinguishable permutations of the letters in the following word.
MISSISSIPPI
4 Ss, 2 Ps, 4 Is
11!/(4!4!2!)
= 11*10*9*8*7*6*5/4*3*2*2 (cancel out!)
=11*5*3*2*7*3*5= 34,650 permutations
500
Find the sum.
(2+1)+(4+1)+(6+1)+(8+1)+(10+1)=35
500
Find the indicated nth partial sum of the arithmetic sequence.
8, 20, 32, 44,.... n=10
a1=8, a2=20 so d=12
a10=a1+9d =8+9(12)=116
S10=(10/2)(8+116)= 620
500
Evaluate the geometric sequence.
a1=(1-29)/(1-2) = 511
500
A shipment of 30 flat screen TVs contains three defective units. In how many ways can a vending company purchase four of these units and receive (a) all good units, (b) two good units, and (c) at least two good units?
There are 27 good sets and 3 defective sets.
(a) 27!/(27-4)!4! = 17,550 ways
(b) 27!/(27-2)!2! * 3!/(3-2)!2! = 351*3 = 1,053 ways
(c) 27!/(27-3)!3! * 3!/(3-1)!1! = 8,775
= 17,550+8,775+1053= 23,378 ways