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.
上一篇: GRE数学单位转换3点注意事项
下一篇: GRE数学单位转换细则
国际英语资讯:2 more Trump campaign staffers at Tulsa rally test positive for coronavirus
国内英语资讯:Chinas annual legislation work plan published
体坛英语资讯:Feature: Cuban athletes train for Tokyo Olympic Games amid COVID-19 outbreak
国际英语资讯:Singapore committed to free flow of goods, services and capital: Deputy PM
国际英语资讯:Egypt values Chinas efforts to promote intl anti-COVID-19 cooperation: FM
国际英语资讯:China hands over medical supplies to Sierra Leone for COVID-19 fight
国内英语资讯:Transactions surge during Chinas mid-year online shopping spree
疫情反弹 美国连续两天单日新增确诊病例超3万
体坛英语资讯:Return of Diamond League offers Kenyan athletes hope, chance to star in athletics
体坛英语资讯:Dortmund ease past rivals Schalke as Bundesliga resumes
国际英语资讯:Roundup: Italys coronavirus outbreak weakens with lowest one-day deaths since March 2
国际英语资讯:Italy records 262 new COVID-19 infections
国内英语资讯:Chinese premier calls on China, EU to expand opening up for mutual benefits
新冠疫情促使非洲网购加速发展
我学会了骑自行车
国内英语资讯:Discover China: Testing starts for domestically-built prototype of new high-speed maglev
体坛英语资讯:Argentina agrees to extend player contracts amid paralysis
国际英语资讯:Three killed, two critically injured in stabbing incident in southern England: police
国际英语资讯:New York City moves into phase two of reopening
国际英语资讯:Africas COVID-19 cases nearly 290,000 as death toll reach 7,693: Africa CDC
体坛英语资讯:Premier League clubs agree to extensions for out-of-contract players
国际英语资讯:Spotlight: COVID-19 cases surge in several U.S. states as reopening efforts continue
国内英语资讯:Spotlight: Hong Kong society welcomes draft law on safeguarding national security in HKSAR
国际英语资讯:Trump fires prosecutor who refused to resign, says U.S. attorney general
福奇:美国出现第二波新冠疫情?第一波还没结束呢
夏至巧遇日环食,这些表达你都知道吗?
体坛英语资讯:Little or nothing will be the same in football: Queiroz
赤壁
国际英语资讯:Turkeys COVID-19 death toll nears 5,000, total cases climb to 187,685
战斗