Sequences

Introduction

• Sequences
  • ordered lists of elements
• Sequence(수열)
  • function from a subset of the integers to a set S
• Term(항) of the Sequence
  • 
  • denoting the image of the integer 𝑛

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Geometric Progression(등비수열)

• a: initial term (초항)
• r: common ratio (공비)
• a&&r: real numbers

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Arithmetic Progression(등차수열)

• a: initial term (초항)
• d: common difference (공차)
• a&&d: real numbers

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Recurrence Relations(점화식)

• an equation that expresses an in terms of one or more of the previous terms of the sequence

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Solving Recurrence Relations

• Finding a closed formula for the nth term of sequence
• Method 1: Working upward
  • forward substitution
  • a2 -> a3 -> a4 -> … -> an = solution
• Method 2: Working downward
  • backward substitution
  • an = an-1 + d = (an-2 +d) +d … = a1 + d(n-1)

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Fibonacci Sequence

• Initial Conditions:

• Recurrence Relation: