GRE数学备考必备考点：算术

　　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=nxdn/2

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

　　example:

　　sum of first 10 positive odd numbers:101+2109/2=10+90=100

　　sum of first 10 multiples of 7 starting at 7： 107+7109/2=70+315=385

　　remember:

　　For a descending AP the constant difference is negative.

　　AP

　　Average of n numbers of arithmetic proGREssion is the average of the smallest and the largest number of them. The average of m number can also be written as x + d/2.

　　Example:

　　The average of all integers from 1 to 5 is /2=3

　　The average of all odd numbers from 3 to 3135 is /2=1569

　　The average of all multiples of 7 from 14 to 126 is /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/2,and the n-th number is s/m + d/2.

　　Example:

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

　　the last number is 70/7+2/2=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+

　　AP:numbers from average

　　all m numbers of an AP can be calculated from the average. the first number x = c-d/2， and the n-th number is c+d/2, where c is the average of m numbers.

　　Example:

　　if the average of 15 consecutive integers is 20, then the first number x=20-1/2=20-7=13 and the last number is 20+1/2=20+7=27.

　　if the average of 33 consecutive odd numbers is 67, then the first number x=67-2/2=67-32=35 and the last number is 67+2/2=67+32=99.

　　Remember:

　　sum of the m numbers is cm,where c is the average.