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Flashcards in Sequences and Sums Deck (18)
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1

sequence

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

2

term

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

3

index

variable k is the index in gvk

4

finite sequence

sequence with finite domain

5

initial index

first index in finite sequence (m)

6

final index

last index in finite sequence (n)

7

initial term

avm

8

final term

avn

9

infinite sequence

sequence with infinite domain, has an initial index of m

10

explicit formula

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..

11

increasing sequence

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

12

non-decreasing sequence

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

13

decreasing sequence

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

14

non-increasing sequence

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

15

geometric sequence

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)

16

common ratio

the fixed ratio for multiplication in a geometric sequence

17

arithmetic sequence

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)

18

common difference

the fixed ratio for adding in a arithmetic sequence