9.1-9.3 sequences and series Flashcards
geometric explicit sequences
an = (a1)r^n-1
geometric recursive sequence
an = r(an-1)
arithmetic recursive sequence
an = a +d
n-1
1st term is positive
(-1)^n+/-1
distinguishable permutations
G R A S S
order matters
taking all elements
set contains indistinguishable elements
5!/ 1! 1! 1! 2! 2!
summation notation alligator teeth face?
right
subset where order doesn’t matter
nCr
n!/(n-r)! r!
arithmetic explicit sequence
an = dn + a0
permutation
order matters
taking all elements
n!
5,6,7,8…
what does “…” mean?
infinite
s = a1/1-r
infinity
subset where order matters
nPr
n!/(n-r)!
combination
order doesn’t matter
taking all elements
arithmetic sum of a series
sn = n/2(a1 + a2)
or an idk?!!!
recursive sequence
provide number equals as part of definition
example: a1 = 4
in addition to the actual equation
1st term negative
(-1)^n
recursive formula
n is in subscripts only
sum of a series geometric
sn = a1(1-r^n/1-r)
Binomial solver with nCr
(x+6)^13
n = power
r =power of term minus 1
C 13 3
Which has a greater amount of possible answers
Permutation or combination?
Permutation because with combination order doesn’t matter so 123 231 321 all count as the same thing (1)
What is “i”
First value of sequence
Usually i equals 1
Find first 4 terms of sequence
Use previous term as “an” to find the next term
Partial sum arithmetic sequence
an = n/2(a1 + an)
