unit 9

Question 1

a function that has as its domain a set of positive integers (1,2,3…n)

Answer 1

sequence

Question 2

an= a1+ (n-1)d

Answer 2

recursive formula, not on reference sheet

Question 3

an= xn + 1

Answer 3

explicit formula (on reference sheet)

Question 4

when a sequence is written in explicit form, plug in the term number to determine the value of the nth term of the sequence

Question 5

recursive formula typically gives a(n) and definiton as to how each successive term is related to the given term

Question 6

writing a sequence in recursive form:
1) include starting value
2) plug in/follow formula format

Question 7

An= (An-1) (r)

Answer 7

geometric sequence format

Question 8

adding/subtracting same value to an arithmetic sequence–> common difference

Question 9

the terms between any two nonconsecutive terms of an arithmetic sequence

Answer 9

arithmetic means (work backwards to find d)

Question 10

sequence that goes from one term to the next by multiplying the same value (common ratio –> r)

Question 11

An= a1r (in exponents–> n-1)

Answer 11

writing geometric sequences in recursive form

Question 12

POSITIVE terms betweenany two nonconsecutive terms of a geometric sequence

Answer 12

geometric means

Question 13

the sum of the terms in a sequence, the formula for the sum of the first n in terms if an arithmetic sequence and is NOT on the formula sheet

Answer 13

series

Question 14

term #
E a1
n= #

Answer 14

or (n-1)d
- find a,then an

Question 15

• involves geometric sequences (multiplication)

Answer 15

200,000 (1+.04/12)

Question 16

An= P (1+r)n - m(1-(1+r) n)/1-(1+r)

Answer 16

Amount owed equation

Question 17

mortgage equation

Answer 17

m= p(r/12) (1+r/12)exponent n

Question 18

Explicit: An= A1r to the power of (n-1)
Recursive: An= (An-1) (r)

Answer 18

geometric explicit vs recursive

Question 19

a1= #
an= (an-1) + d

Answer 19

recursive formula for arithmetic sequence

Question 20

a1=#
an= r (an-1)

Answer 20

recursive formula for geometric sequence

Question 21

an= a1+ (n-1)d
used to find terms of things, etc.

Answer 21

General term for arithmetic sequence

Question 22

• terms between any two non consecutive terms of an arithmetic sequence
• find a1
• solve for d
• plug in and solve

Answer 22

arithmetic means

Question 23

• positive terms between any two nonconsecutive terms of a geometric sequence
• use a1(r) to the power of n-1

Answer 23

geometric mean

Question 24

recursive= an-1 + d
explicit- an= a1 + (n - 1) d

Answer 24

explicit & recursive arithmetic formula