俗話說：“工欲善其事必先利其器”。很多參加了新版GRE考試的同學(xué)都覺得數(shù)學(xué)有點難度，相信這其中的原因還是由于考生在新版gre數(shù)學(xué)復(fù)習(xí)時沒有把基礎(chǔ)打牢。如果新版gre數(shù)學(xué)基本考點都沒有復(fù)習(xí)到，如何能拿到分數(shù)呢?所以說，想要新版gre數(shù)學(xué)考好，復(fù)習(xí)的時候一定要把基本概念和重要考點都弄扎實。
今天針對新版gre數(shù)學(xué)復(fù)習(xí)，小編給大家整理的是關(guān)于平均數(shù)的相關(guān)內(nèi)容，這些概念在考試中一定會考到的。希望考生能再接再厲，取得一個好成績，突破新版gre數(shù)學(xué)難的困境。
新版gre數(shù)學(xué)復(fù)習(xí)重要考點：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.
很多新版gre數(shù)學(xué)復(fù)習(xí)考點都是高中時候?qū)W到的知識點，考生不要過于緊張，把基本概念弄明白，再記住一些新版gre數(shù)學(xué)必備的詞匯，那么相信新版gre數(shù)學(xué)應(yīng)該沒有問題。
今天針對新版gre數(shù)學(xué)復(fù)習(xí)，小編給大家整理的是關(guān)于平均數(shù)的相關(guān)內(nèi)容，這些概念在考試中一定會考到的。希望考生能再接再厲，取得一個好成績，突破新版gre數(shù)學(xué)難的困境。
新版gre數(shù)學(xué)復(fù)習(xí)重要考點：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.
很多新版gre數(shù)學(xué)復(fù)習(xí)考點都是高中時候?qū)W到的知識點，考生不要過于緊張，把基本概念弄明白，再記住一些新版gre數(shù)學(xué)必備的詞匯，那么相信新版gre數(shù)學(xué)應(yīng)該沒有問題。