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Math
| Question | Answer |
|---|---|
| sequece | a fuction that computes an ordered list |
| finite sequence | set of natural numbers of the form {1,2,3...n} as domain |
| infinite sequence | set of naturals as domains ---> goes on forever |
| converge | gets closer to some real number -approach |
| diverge | never approaches -no limit |
| recursion formula | builds each other |
| Arithmetic | a set of numbers that have a common difference (d) |
| arithmetic sequence formulas (to find a specific term) | nth term: An = Ab + (n - b) d -ALWAYS put the bigger number on the left (An) and the smaller one on the right (Ab) |
| when asked to find the formula for An, | make sure to distriute the d when simplifying |
| when asked to find the sum of the terms of an arithmetic sequence | Sn = n/2 (A1 + An) OR Sn = n/2 [2A1 + (n-1)d] |
| Geometric | a sequence in which each term is multiplied by a common ratio (r) |
| what is the nth term in a geometric sequence (equation) | An = A1 * r^(n-1) |
| the sum of the first n terms in a geo series is | Sn = A1 (1 - r^n) divided by 1 - r r cannot be equal to one for this equation |
| sum of the number of terms of an infinite geo sequence | S inf = A1/(1-r) |r| < 1 if |r|> 1 then there is no sum |
| sigma/summation nation | b ∑ f(i) i=a -plug a into the function, A1 or your starting point is the # found after plugging in a -counting by ones, plug in different #s in order until you end by plugging in b -find n: top # - bottom # +1 -then solve like normal |
| if you are given a percent for a geometric word problem, then | r = the percent (changed into a decimal) that remains |
| factorials | you multiply the number by every number below it (stopping at 1) |
| pascal's triangle | The top is 1 Every # is the sum of the 2 #s above it The edges are always 1 1 1 1 1 2 1 1 3 3 1 each row corresponds to the power of the binomial (top row is row 0) -the #s are coefficents of the expanded binomial |
| when finding the expanded version of a binomial using pascal's triangle, how to find the power of ecah term in the binomial | the first term in the binomial is your decreasing power (start with the power of the binomial) the second is the increasing (start with zero) |
| when finding the expanded version of a binomial using pascal's triangle, how to multiply to find your answer | write the pascell's row of numbers beheath each number, write the first term and then the second term directly below each other -multiply each colum (note, negitive numbers are in (-#)^2) -then add each product together |
| how to find a specific term (like the 10th) in an expanded binomial (how to find the power of each term) | -sum of the 1st term's power and 2nd = the power of the binomial -subtract the term number from the binomial's power |
| how to find a specific term (like the 10th) in an expanded binomial (formula in words) | take the factorial of the power of the binomial & divide by the product of the factorial of the power of the 1st term and the 2nd term. multiply by the 1st term to the power of the given number times the second term to the power solved for |
| how to find a specific term (like the 10th) in an expanded binomial (formula ) | For (a + b)^n, the (r + 1)th term is: T(r+1) = n! / [(n − r)! r!] · (term 1)^(n − r) · (term 2)^r n = power of the binomial r = the given power |
| for some equations you can replace the A1 with a different term in the sequence and replace 1 with the new term's number. Why does this only work for some equations | All geometric or arithmetic term equations work cause d is constant (the difference between two consecutive terms in the sequence is always the same) -but for Sn, the sequence is not linear |
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Blessed Rectangle 10