Sequences & Series

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Author:
jojobean0203
ID:
230549
Filename:
Sequences & Series
Updated:
2013-08-20 03:04:23
Tags:
calc
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Description:
calc
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  1. relation between consecutive terms:
    arithmetic sequence
    geometric sequence
    • arithmetic: difference
    • geometric: ratio
  2. to find nth term of arithmetic sequence, need either:
    • 1 term & distance
    • 2 terms
  3. to find nth term of geometric sequence, need either:
    • 1 term & common ratio
    • 2 terms
  4. arithmetic sequence:
    general formula for nth term
    an = a1 + (n-1)d
  5. arithmetic sequence: recursive formula for nth term
    an = an-1 + d
  6. formula to add first n terms of an arithmetic sequence if a1, an, & n are known
  7. formula to add first n terms of an arithmetic sequence if an unknown
  8. geometric sequence: general formula for nth term
    an = a1 r n-1
  9. geometric sequence: recursive formula for nth term
    an = r an-1
  10. formula to add first n terms of a geometric sequence as long as r  1
  11. formula to add first n terms of a geometric sequence when -1 < r < r & r0
  12. to make odd terms in a sequence negative, use factor:
    (-1)n
  13. to make even terms in a sequence negative, use factor:
    (-1)n+1
  14. how to determine ratio of a geometric sequence
    • term multiplied by a constant equals the next term
  15. when is the sum of all the terms in a geometric sequence equal to a number?
    when common ratio is small: -1 < r < 1
  16. difference between infinite sum formula & partial sum formula
    the 1-rn in the numerator of the partial sum formula is replaced by 1 in the numerator of the infinite sum formula

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