sequences and series Flashcards
what is an arithmetic progression?
sequence where terms increase or decrease by a common difference each time
what do the following terms mean?
a
d
Un
Sn
a = first term
d = common difference
Un = nth term
Sn = sum of first n terms
what is the formula for nth term?
(not given)
Un = a + (n-1) d
what is the proof of the Sn formula?
what is a sequence?
a set of numbers in a given order which may follow an algebraic pattern
what is suffix notation?
where each term in a sequence is denoted by a letter (the same for every term) with a subscript which gives the term’s position
what is a sequence deefined by?
its nth term - known as its general term - in an arithmetic progression this can be calculated directly from its position in the sequence
what is an inductively defined sequence?
each term (Un+1) is calculated from the previous term. to start, the first term (U1) or U0 is needed:
Un+1 is found by putting Un (current term) into the equation.
what does increasing mean?
each term greater than the one before
what does decreasing mean?
each term less than one before
what does periodic mean?
set of n terms repeat indefinitely (so have an order n)
what does convergent mean?
terms of sequence approch a limit
what doe alternating/oscillating mean?
terms alternatively increase and decrease, not necessarily between same values
what does divergent mean?
not convergent
what is a series?
when the terms of a sequence are added together
adding up the first n terms is called Sn
what is sigma notation?
