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)

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## index

### variable k is the index in gvk

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## finite sequence

### sequence with finite domain

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## initial index

### first index in finite sequence (m)

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## final index

### last index in finite sequence (n)

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## initial term

### avm

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## final term

### avn

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## infinite sequence

### sequence with infinite domain, has an initial index of m

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## 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..

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## increasing sequence

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

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## non-decreasing sequence

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

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## decreasing sequence

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

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## non-increasing sequence

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

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## 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)

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## common ratio

### the fixed ratio for multiplication in a geometric sequence

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## 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)

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