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# recursive and explicit formulas

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## Arrin Smith

on 4 January 2013

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#### Transcript of recursive and explicit formulas

math project
recursive and explicit formulas recursive formulas an = an-1 + d arithmetic formula: you need to know the previous term to be able to determine the answer geometric formula: an = r(an-1) a1 = first term in the sequence
an = the nth term
an-1 = the term BEFORE the nth term
d = common difference (could be negative)
r = common ratio (could be fraction) arithmetic example:
-4, -6, -8, -10 recursive: an=an-1+d
an=an-1 -2
a(5)=(-10)-2
a(5)=-12
a(6)=(-12)-2
a(6)=-14
a(7)=(-14)-2
a(7)=-16 -4, -6, -8, -10, -12, -14, -16 geometric example: 25, 75, 225 recursive formula an=r(an-1) ratio term after over term before an=3(an-1) a(4)=3(225)
a(4)=675
a(5)=3(675)
a(5)=2025 25, 75, 225, 675, 2025 explicit based on the term number arithmetic formula: geometric formula: an = a1 + d(n – 1) an = a1(r^n-1) a1 = first term in the sequence
an = the nth term
an-1 = the term BEFORE the nth term
d = common difference (could be negative)
r = common ratio (could be fraction) arithmetic example explicit -4, -6, -8, -10 an= a1+d(n-1) an=-4-2(n-1) a(5)=-4-2(4)
a(5)=-4-8
a(5)=-12
a(6)=-4-2(5)
a(6)=-4-10
a(6)=-14 -4, -6, -8, -10, -12, -14 an = a1(r^n-1) geometric example explicit 25, 75, 225 an = 25(3^n-1)
a(4)=25(3^3)
a(4)=25(27)
a(4)=675
a(5)=25(3^4)
a(5)=25(81)
a(5)=2025 25, 75, 225, 675, 2025 Richard Bjorneby
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