sequences and series Flashcards
what is a deductive sequence formula
when the formula allows you to find any position term (position-to-term rule)
what is an inductive sequence formula
a formula that tells you how to find each term of a sequence from the previous term (term-to-term rule or recurrence relation)
what are arithmetic sequences
linear
have a common difference
what are quadratic sequences
have a common second difference
an^2+bn+c
what are geometric sequences
have a common ratio
(can be negative so it fluctuates from +-+-)
what are fibonacci or fibonacci type sequences
a(n+2) = a(n) + a(n+1)
what are increasing or ascending sequences
each term is greater than the preceding term
what are decreasing or descending sequences
each term is less than the preceding term
what are alternating sequences
each term switches from positive to negative +-+-+-
what is a periodic sequence and a period
with a repeated pattern, the period is how many terms in the repeat
what are divergent sequences
differences increasing (terms getting further away)
what are converging sequences
differences are decreasing (terms are getting closer to or tending to a limit) but it never reaches the limit
what is an oscillating sequence
oscillated around a number, from one side of it to the other, with the same difference for each side of the number, can get closer to the number or further away
what is a1
first term
what is l
last term
what is n
number of terms
what is d
common differende
what is S4
sum of first four terms
what is Sn
sum of all the terms
what is r
common ratio
