Topic 1: Algebra Flashcards
What is an an arithmetic sequence?
A sequence(list) of numbers with a common difference (the same difference between each term in the list)
How to calculate common difference in an arithmetic sequence
d=u2 - u1 where u=term
or any term minus the term before it
Finite vs infinite sequence
Finite has an ending term, infinite continues forever
What does the letter “n” mean in terms of arithmetic sequences?
It is the place that the term falls in the sequence
When to use which formula to calculate the sum of n terms of an arithmetic sequence?
use second formula when you know un (ex: if asking for S10 and you know u10, use second formula).
if you don’t know un, use first formula.
What is an arithmetic series?
The sum of the terms of an arithmetic sequence
What is a geometric sequence?
A sequence (list) of numbers with a common ratio between each term
How to determine the common ratio of a geometric sequence
r = u1/u2
or any term divided by the term before it
if the numbers in the sequence alternate between negative and positive, you know the common ratio is negative
When can you find the sum of an infinite geometric sequence?
When the common ratio is between 1 and -1 (smaller in value than 1), which means the numbers in the sequence are getting smaller and smaller making the value of the sum converge.
What is a geometric series?
The sum of a geometric series
What does ln mean
log base e
