Sequences and Sums

Question 1

sequence

Answer 1

special type of function, domain is a consecutive set of integers

Question 2

term

Answer 2

use subscripts to denote the input to the function so gvk instead of g(k)

Question 3

index

Answer 3

variable k is the index in gvk

Question 4

finite sequence

Answer 4

sequence with finite domain

Question 5

initial index

Answer 5

first index in finite sequence (m)

Question 6

final index

Answer 6

last index in finite sequence (n)

Question 7

initial term

Answer 7

avm

Question 8

final term

Answer 8

avn

Question 9

infinite sequence

Answer 9

sequence with infinite domain, has an initial index of m

Question 10

explicit formula

Answer 10

a sequence specifically showing how the value of term avk depends on k eg. dvk = 2k for k ≥ 1, starts with: 2,4,8,16..

Question 11

increasing sequence

Answer 11

increasing if for every two consecutive indices, k and k+1, in the domain, avk < avk+1

Question 12

non-decreasing sequence

Answer 12

if for every two consecutive indices, k and k+1, in the domain avk <= avk+1

Question 13

decreasing sequence

Answer 13

if for every two consecutive indices in the domain avk > avk+1

Question 14

non-increasing sequence

Answer 14

if for every two consecutive indices in the domain avk >= avk+1

Question 15

geometric sequence

Answer 15

sequence of real numbers where each term after the initial term is found taking the previous term and multiplying by a fixed number (common ratio)

Question 16

common ratio

Answer 16

the fixed ratio for multiplication in a geometric sequence

Question 17

arithmetic sequence

Answer 17

sequence of real numbers where each term after the initial term is found by taking the previous term and adding a fixed number (common difference)

Question 18

common difference

Answer 18

the fixed ratio for adding in a arithmetic sequence