Sequences & Series

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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
 Author: jojobean0203 ID: 230549 Card Set: Sequences & Series Updated: 2013-08-20 07:04:23 Tags: calc Folders: Description: calc Show Answers: