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Geometric Sequences Skill 50
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Objective HSF-BF.2: Write geometric sequences both recursively and with an explicit formula, use them to model situations and translate between two forms.
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The Geometric Sequences
Starting Value = a Common Ratio = r π, πβπ, πβπβπ, πβπβπβπ,β¦ π, ππ, π π 2 , π π 3 ,β¦ Recursive Formula: π 1 =π π π = π πβ1 βπ π π =β¦ Explicit Formula: π π = π 1 β π πβ1
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Example; Geometric Sequence
Is the sequence Geometric or Arithmetic? 2, 4, 6, 8, 10,β¦ +2 +2 +2 +2 The sequence is Arithmetic because there is a common difference, not a common ratio. 5, β5, 5, β5, 5,β¦ x(-1) x(-1) x(-1) x(-1) The sequence is Geometric because there is a common ratio (-1) between terms.
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Example; Geometric Sequences
Find a recursive and explicit formula. 7, 21, 63, 189,β¦ π= 21 7 =π Recursive Formula. π 1 =β¦ π π = ππππ£πππ’π β¦ Explicit Formula. π π =π π π =β¦ π π = π πβπ βπ π π = π 1 β π πβ1 π π =π π πβπ
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Example; Geometric Sequences
Two managers at a clothing store created sequences to show the original price and the marked-down prices of an item. Write an explicit formula for each sequence. Find the price of the item be after the 6th markdown. $60, $51, $43, $36.85,β¦ $60, $52, $44, $36,β¦ π= =$π.ππ π=52β60=β$π π π = π 1 +π πβ1 π π = π 1 β π πβ1 π π =60β8 πβ1 π π =ππ π.ππ πβπ π π =60β8π+8 π π =βππ+ππ π 7 = β1 π 7 =β π π =$ππ.ππ π π =$ππ.ππ
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#50: Geometric Sequences
Questions Summarize Notes Homework Google Classroom Quiz
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