Arithmetic and geometric formulas

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11 Terms

1
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What is a sequence?

1, 2, 3, 4…

2
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What is a series?

1+2+3+4+….+10

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Explicit Arithmetic

an = a1 + (n-1)•d

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Recursive Arithmetic

an= { a1 ; n=1

……..an-1 + d ; n>1

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Explicit Geometric

an = a1•r^n-1

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Recursive Geometric

an = { a1 ; n=1

………an-1•r ; n>1

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Sum of Finite Arithmetic Series

Sn = n (a1 + an)/2

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Sum of finite geometric series

Sn = a1 (1-r^n)/(1-r)

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Sum of infinite geometric series

|r|<1 ONLY, if |r|>1 then No Sum

Sn = a1/(1-r)

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Sigma notation arithmetic

n S i=1 a1 + d

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Sigma notation geometric

n S k=1 a1•r^k-1