Chpt. 9, Sequences and Series

Question 1

sequence

Answer 1

an ordered list of numbers

Question 2

term of a sequence

Answer 2

any number in a sequence

Question 3

explicit formula

Answer 3

expresses the nth form of a sequence in terms of n

Question 4

recursive formula

Answer 4

defines each term in a formula by relating it to the ones before it

Question 5

arithmetic sequence

Answer 5

a sequence with a constant difference between consecutive terms

(a, b, c, d, etc)

Question 6

common difference

Answer 6

the difference between terms of an arithmetic sequence

Question 7

arithmetic mean (of two numbers)

Answer 7

the sum of the numbers divided by two

Question 8

geometric sequence

Answer 8

a sequence with a constant ratio between consecutive terms

a, ar, ar^2, ar^3, ar^4, etc

Question 9

common ratio

Answer 9

the ratio of consecutive terms of a geometric sequence

Question 10

geometric mean (of two numbers)

Answer 10

the positive square root of the product of the two numbers

Question 11

series

Answer 11

the sum of the terms of a sequence

Question 12

finite series

Answer 12

a series with a finite number of terms

Question 13

infinite series

Answer 13

a series with infinitely many terms

Question 14

arithmetic series

Answer 14

a series whose terms form an arithmetic sequence

Question 15

limits

Answer 15

the least and greatest integer values of the index n

Question 16

geometric series

Answer 16

the sum of the terms in a geometric sequence

Question 17

converge (of a geometric series)

Answer 17

to get infinitely closer to a real number as the value of n increases

Question 18

diverge (of a geometric series)

Answer 18

to grow exponentially; this is what all geometric series do if they do not converge

Question 19

what does the sigma look like?

Answer 19

an “”

Question 20

what goes on top of the sigma

Answer 20

b, that is, which is the upper bound of n-values for the sequence

(on top, upper bound)

Question 21

what goes on bottom of the sigma

Answer 21

x = a, in which a stands for the first n-value of the sequence

(on bottom, lower bound)

Question 22

what goes in front of the sigma

Answer 22

the equation into which the n-value is plugged

Question 23

how to find the common ratio (r) of a geometric sequence

Answer 23

(sub2asub1 = (asub3/asub2) = (asub47/asub46) = (asubn/asubn-1)

Question 24

recursive, arithmetic, consecutive terms

Answer 24

asub(n-1) = asub(n) + d

Question 25

(explicit?), arithmetic, non-consecutive terms

Answer 25

asub(n) = asub(1) + (n-1)d

Question 26

sum of arithmetic terms

Answer 26

Ssub(n) = n/a(asub(1) + asub(n))

Question 27

sum of arithmetic terms, alternate formula

Answer 27

Ssub(n) = n/2 (asub1 + (asub1 + (n-1)d))

Question 28

recursive, geometric, consecutive terms

Answer 28

asub(n +1) = asub(n) * r

Question 29

explicit, geometric, non-consecutive terms

Answer 29

asub(n) = asub(1) * r^n-1

Question 30

sum of geometric terms

Answer 30

Ssub(n) = asub(1) * (1-r^n)

—–all over—–

1 - r