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# Numeric and Geometri

### Numeric and Geometric Patterns

TermDefinition
perimeter of circle 2PIr
area of parallelogram base times height
V of cylinder PIr^2h
area of circle PIr^2
SA of sphere 4PIr^2
V of sphere 4/3 PIr^3
SA of cone PIrs+PIr^2
V of cone 1/3 PIr^2h
SA of square pyramid 2bs+b^2
V of square pyramid 1/3 b^2h
V of triangular prism (not equilateral) 1/2 blh
A of trapezoid ((a+b)h)/2
What is the difference between a finite sequence and infinite sequence? An infinite sequence never ends, a finite sequence has an end.
What is one way to find the limit of a sequence? A coordinate graph (graphing the sequence)
How do you solve for problems with subscripts? (asking to find the 3rd and 12th term) You must plug in the number(which is subscript) for n in the equation and solve (3 plugged in for n and 12 plugged in for 12)
What is an arithmetic sequence? When you add or subtract a certain(constant) amount to get to the next term (d- common difference, used to represent this constant number)
What is a geometric sequence? When you multiply or divide a certain(constant) amount to get to the next term (r- common ratio, used to represent this constant number)
What form does arithmetic sequences follow? a¹+d(n-1)
What form does geometric sequences follow? aᴺ=a¹rᴺ-¹
How do you find the common ratio of a sequence? r=aᴺ/aᴺ-¹
How do you find the common difference of a sequence? d=aᴺ-aᴺ-¹
What formula do you use to find the number of terms in a finite arithmetic sequence? aᴺ=a¹+d(n-1) (n is the final term in aᴺ)
When the terms of a sequence are added together, what is the sum of the terms called? a series
If the sequence of partial sum of an infinite series has a limit, then that limit is... the sum of the series
The sum of the first "n" terms of an infinite series is called a... partial sum (of the series)
When you are solving for sigma notation problems and they are in the form of an arithmetic sequence, then you can use the formula ... ? sᴺ=n(a¹+aᴺ)/2 (you still have to find the first and last term before plugging it into the formula)
When you are solving for sigma notation problems and they are in the form of a geometric sequence, then you can use the formula ... ? S=a¹-aᴺr/1-r (aᴺ is the last term of the series)
What is the formula and way of solving an arithmetic series? You must use the formula aᴺ=a¹+d(n-1) to find the number of terms in the series, next you must take that number of terms and plug it into the formula: sᴺ=n(a¹+aᴺ)/2 (both the sᴺ and n are representing the number of terms which were previously found)