Studied by 2 people
Un
n is the position of the term in the sequence
U1
first term
Finding the general term
Un = n
recursive sequences
uses the previous term or terms to find the next term. The general term will include the notation Un-1 which means the previous term.
Sigma notation
upper limit can be infinite
The formula for any term in an arithmetic sequence is also known as explicit formula
un= u1 + (n-1) d
to find a term of an arithmetic sequence given two other terms
change the -1 to whatever term number you want to find!!!! then find the difference and substitute that into the equation
Formula to find any term in a geometric sequence is also know as the explicit formula
Un = U1r^n-1
The formula for the sum of an arithmetic series is
Sn = (n/2) [2u1 + (n - 1) d]
The formula for the sum of a geometric series
Sn = u1(r^n - 1)/ r-1
sum of a converging (r between -1 and 1) infinite geometric series
Sn = u1/1-r
Meaning of variables in interest equations
A= accumulated amount: future amount
P= Principal
r= annual rate
n= years
t= total number of years
BUTT for compound interest over a non year period
n is equal to the how often do if it’s semi annually n=2, quarterly n= 4, monthly = 12, weekly = 52 etc
Formula for simple interest
A= P(1+nr)
formula for compound interest
A= P(1+r)^n
Compound interest over non year period
A= P(1+ r/n) ^nt
Recursive formula
Un = Un-1
add a number or subtract if arithmetic, multiply or divide a number if geometric
