新GRE数学要点:AP

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AP 　　Average of n numbers of arithmetic progression (AP) is the average of the smallest and the largest number of them. The average of m number can also be written as x + d(m-1)/2.
　　Example:
　　The average of all integers from 1 to 5 is (1+5)/2=3
$ e. p: b6 g9 m( j  X5 W+ ^　　The average of all odd numbers from 3 to 3135 is (3+3135)/2=1569
　　The average of all multiples of 7 from 14 to 126 is (14+126)/2=70
　　remember:
$ t8 M: [9 i2 \# ]8 e4 o/ S　　Make sure no number is missing in the middle.
6 I3 x, B! E5 \% _1 H$ \; A' u# y　　With more numbers, average of an ascending AP increases.
1 s, S: B! |1 ~( s9 h　　With more numbers, average of a descending AP decreases.
　　AP:numbers from sum
) V+ v9 {7 x* C: W% }　　given the sum s of m numbers of an AP with constant increment d, the numbers in the set can be calculated as follows:
% L9 u& ^& t/ c" K1 X　　the first number x = s/m - d(m-1)/2,and the n-th number is s/m + d(2n-m-1)/2.
: ^$ G' ]1 W4 W- ?3 L/ z　　Example:
/ _9 e- k  ~2 Q  \/ e5 ?+ P4 K　　if the sum of 7 consecutive even numbers is 70, then the first number x = 70/7 - 2(7-1)/2 = 10 - 6 = 4.
& [1 T  b, H! y8 h% G　　the last number (n=m=7)is 70/7+2(2*7-7-1)/2=10+6=16.the set is the even numbers from 4 to 16.
" C9 ~7 }* [  n8 p　　Remember:
　　given the first number x, it is easy to calculate other numbers using the formula for n-th number: x+(n-1)
　　AP:numbers from average
　　all m numbers of an AP can be calculated from the average. the first number x = c-d(m-1)/2, and the n-th number is c+d(2n-m-1)/2, where c is the average of m numbers.
' \) P1 K6 r) P# P3 r6 l- K7 k　　Example:
　　if the average of 15 consecutive integers is 20, then the first number x=20-1*(15-1)/2=20-7=13 and the last number (n=m=15) is 20+1*(2*15-15-1)/2=20+7=27.
' [& D  ^  t5 A. c4 \　　if the average of 33 consecutive odd numbers is 67, then the first number x=67-2*(33-1)/2=67-32=35 and the last number (n=m=33) is 67+2*(2*33-33-1)/2=67+32=99.
　　Remember:
　　sum of the m numbers is c*m,where c is the average.
9 n) g  E7 O1 V/ i+ s　　由于美国数学基础教育的难度增加导致数学考试越来越难，但新gre数学复习考点都是高中时候学到的知识点，考生不要过于紧张，把基本概念弄明白，再记住一些新版gre数学必备的词汇，那么相信新版gre数学应该没有问题。