Sequences Flashcards
Explain sigma notation.
Start at the bottom value.
End at the value on top.
The thing on the right is what you sum up to.
Define arithmetic sequence.
An ordered list of numbers that have a common difference , d.
What is a geometric sequence?
A geometric sequence is an ordered list of numbers changing by a common ratio.
How do you use sum to infinity to show an infinite recurring decimal is a fraction. Use 0.454545… as an example.
You can think of it as a geometric sequence that goes 0.45, 0.0045, 0.000045…
Find the sum to infinity using 0.01 as a common ratio.
Turn you result into a fraction in its simplest form.
How are stationary points found?
There are where dy/dx = 0
What are increasing or decreasing functions?
An increasing function has a positive gradient for the specified x values. A decreasing function is the same but the gradient is negative.
How are points classified using higher derivatives ?
Greater than 0. A minimum.
Less than 0. A maximum.
Explain the notation used then doing sequences.
d= the common difference of an arithmetic sequence. a= first term. l= last term. n= number of terms. r= common ratio.
How is a certain term in an arithmetic sequence found?
a+(k-1)d. If you wanted to find the fifth term, you would multiply d by 4 and add this to a.
How would you find the last term in an arithmetic sequence?
a+(n-1)d. n being the number of terms.
How is the sum of n terms in an arithmetic sequence found?
sum of n terms=0.5n(2a+(n-1)d)
How is a certain term in a geometric sequence found?
a X r^k-1
If you wanted to find the fifth term, put the common ratio to the power of 4 and multiply this by a.
How is the sum of terms in a geometric sequence found?
(a(r^n-1))÷r-1
(a(1-r^n))÷1-r
How is the sum to ∞ found?
a÷(1-r)
