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sequence+series (sequence (arithmetic (\(n^{th}\) term (\(a+(n-1)d\),…

- - - - \(a+(n-1)d\)
      - d=difference
  - - - \(ar^{n-1}\)
- - - - \(\frac{n(n+1)}{2}\)
  - - - \(\frac{a}{1-r}\)

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sequence+series

arithmetic

sequence

series

infinite

finite

list of numbers

when we add terms of sequence

arithmetic

increase by the same amount every term

$n^{th}$ term

\(a+(n-1)d\)

d=difference

arithmetic

number of terms*average of 1st and last term

first n numbers

\(\frac{n(n+1)}{2}\)

sum of first n odd integers \(n^2\)

geometric

common ratio between terms

\(n^{th}\) term

\(ar^{n-1}\)

geometric

sum: n. terms, first term a and common ratio r

\(\frac{a(r^n-1)}{r-1}\)

infinite geometric series

\(\frac{a}{1-r}\)