新版GRE数学复习重要考点:Sum of Arithmetic ProGREssion

　　The sum of n-numbers of an arithmetic proGREssion is given by

　　S=nx*dn(n-1)/2

　　where x is the first number and d is the constant increment.

　　example:

　　sum of first 10 positive odd numbers:10*1+2*10*9/2=10+90=100

　　sum of first 10 multiples of 7 starting at 7: 10*7+7*10*9/2=70+315=385

　　remember:

　　For a descending AP the constant difference is negative.

　　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。

　　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

　　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:

　　Make sure no number is missing in the middle.

　　With more numbers, average of an ascending AP increases.

　　With more numbers, average of a descending AP decreases.

　　AP:numbers from sum

　　given the sum s of m numbers of an AP with constant increment d, the numbers in the set can be calculated as follows:

　　the first number x = s/m - d(m-1)/2,and the n-th number is s/m + d(2n-m-1)/2.

　　Example:

　　if the sum of 7 consecutive even numbers is 70, then the first number x = 70/7 - 2(7-1)/2 = 10 - 6 = 4.

　　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.

　　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.

　　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.

　　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.

　　以上是为大家整理的新GRE数学重要考点知识，希望能给新GRE考生带来一定的帮助。