Series / Sequences / Recursive / Explicit

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an=an-1+d
arithmetic recursive
an=a1+(n-1)d
arithmetic explicit
an=an-1(r)
geometric recursive
an=a1(r)^(n-1)
geometric explicit
When order matters, use... (How many different possibilities?)...
nPr
When order does NOT matter, use... (How many different possibilities?)...
nCr
There are 10 marbles in a bag: 1 red, 1 white, 1 yellow, 2 green, 2 blue, and 3 orange. (How many different possibilities?)
...
(n/2)(2a1+(n-1)d)
arithmetic summation formula
(a1(1-n^r)) / (1-n)
geometric summation formula
In a summation, when i or k is greater than 1... (fill in the blank) Take the normal answer of k=1 and n= the original n, and then find the same summation where k=1 and n is 1 less than the original given k. Then you _______ the summation with the different n from the summation with the original n to find the final answer.
subtract
(n*(n+1))/2
Summation of k
(n*(n+1)(2n+1))/6
Summation of k^2
((n^2)*(n+1)^2)/4
Summation of k^3
limit = (a1)/(1-r)
geometric converging limit
When finding n for a series in order to find the series' summation, what type of geometric/arithmetic formulas can you plug the given numbers in to find n?
explicit
When finding n for a series in order to find the series' summation, what type of geometric/arithmetic formulas should you NOT use to plug in the given numbers in to find n?
recursive