sequences and combinatrics

Question 1

n^th term of an arithmetic sequence

Answer 1

n= term number, d = difference

a_n = a₁ + (n-1) d

Question 2

Combination - Unordered

Answer 2

. n! .

k! (n-k)!

k items selected from a total of n items

Question 3

Permutation - ordered

Answer 3

_ n! _

(n-k)!

Question 4

Percent Change

Answer 4

Percent Change =

Change in Value

Original Value

Question 5

Function

Answer 5

y = f(x)

x = input

y = output

Question 6

Groups

Answer 6

G₁ + G₂+ Neither - Both = Total

Question 7

Combined Work Formula

Answer 7

product of independent time

sum of those times

= time working together

Question 8

in an evenly spaced set:

Answer 8

mean = median

both are the average of the first and last term

sum equals the mean times the number of terms

Question 9

The number of terms in consecutive multiples:

Answer 9

Last - First

(incremental change) +1

Question 10

consecutive integers

Answer 10

average of an odd # of consecutive integers is an integer

average of an even # of consecutive integers will not be an integer

Question 11

Rate =

Answer 11

_Distance _

Time

= rate

Question 12

Distance

Answer 12

Distance = Rate x Time

Question 13

Sum of an ODD # of consecutive integers

Answer 13

is always a multiple of the # of items

Question 14

The product of K consecutive integers

Answer 14

is always divisible by K!

Question 15

Sum of an even # of consecutive intergers is

Answer 15

never a multiple of the number of items.

Question 16

for any perfect square

Answer 16

the prime factors pair up

Question 17

3! =

4! =

5! =

6! =

Answer 17

3! = 6

4! = 24

5! =120

6! = 720

Question 18

If members of a group are identical then

Answer 18

divide the total number of arrangements by 2!

Question 19

Combinations with identical members

Answer 19

_ n! _