Chapter 20 - Sequences and Series (Pure) Flashcards
what does Un mean?
Un is the nth term of a sequence
what’s an increasing function?
an increasing function is when each term is larger than the previous term
Uk+1 is bigger than Un
what is a decreasing function?
a decreasing sequence is when each term is smaller than the last
Uk+1 is less than Uk
what’s a periodic sequence?
a periodic sequence is when the terms repeat in a cycle
whats an arithmetic sequence?
adding or subtracting a fixed amount.
what’s an arithmetic sequence equation?
Un = a + (N-1)d
a is the first term
d is the amount added each time
n is the position of any term.
the arithmetic series sum of equation is found on the data sheet.
Sn = 1/2 n [2a + (n-1)d] = 1/2 n (a+ L)
Sn = 1/2 n [2a + (n-1)d] = 1/2 n (a+ L)
a= first term
n= is the position of the term
d= is the difference
l= is the last term
what does Σ mean?
Σ means the sum of
15
Σ (2n +3)
n=1
15 means the last n is 15 from 1 to 15
what are natural numbers ? what is the sum of them?
natural numbers are positive whole numbers i.e 1,2,3,4,5
Sn= 1/2 n (n+1)
what’s a geometric sequence? what’s the formula?
a geometric sequence is multiplication by a common constant r
Un = ar ^(n-1)
a= first term
r= common ratio
the sum of a geometric series equation is found on the data sheet, what do the symbols stand for?
Sn= a(1-rⁿ)/ 1-r
Sn= a(1-rⁿ)/ 1-r
a is the first term
r is the common ratio
n is the term number
